Combinatorial Games: Selected Bibliography with a Succinct Gourmet Introduction

Aviezri S. Fraenkel

Department of Applied Mathematics and Computer Science

Weizmann Institute of Science Rehovot 76100, Israel

             fraenkel@wisdom.weizmann.ac.il
       http://www.wisdom.weizmann.ac.il/∼fraenkel

1 What are Combinatorial Games?

Roughly speaking, the family of combinatorial games consists of two-player games with perfect information (no hidden information as in some card games), no chance moves (no dice) and outcome restricted to (lose, win), (tie, tie) and (draw, draw) for the two players who move alternately. Tie is an end position such as in tic-tac-toe, where no player wins, whereas draw is a dynamic tie: any position from which a player has a nonlosing move, but cannot force a win. Both the easy game of nim and the seemingly difficult chess are examples of combinatorial games. And so is go. The shorter terminology game, games is used below to designate combinatorial games.

2 Why are Games Intriguing and Tempting?

Amusing oneself with games may sound like a frivolous occupation. But the fact is that the bulk of interesting and natural mathematical problems that are hardest in complexity classes beyond NP, such as Pspace, Exptime and Expspace, are two-player games; occasionally even one-player games (puzzles) or even zero-player games (Conway’s “Life”). Some of the reasons for the high complexity of two-player games are outlined in the next section. Before that we note that in addition to a natural appeal of the subject, there are applications or connections to various areas, including complexity, logic, graph and matroid theory, networks, error-correcting codes, surreal numbers, on-line algorithms, biology — and analysis and design of mathematical and commercial games!

But when the chips are down, it is this “natural appeal” that lures both amateurs and professionals to become addicted to the subject. What is the essence of this appeal? Perhaps the urge to play games is rooted in our primal beastly instincts; the desire to corner, torture, or at least dominate our peers. A common expression of these vile cravings is found in the passions roused by local, national and international tournaments. An intellectually refined version of these dark desires, well hidden beneath the façade of scientific research, is the consuming drive “to beat them all”, to be more clever than the most clever, in short — to create the tools to Mathter them all in hot combinatorial combat! Reaching this goal is particularly satisfying and sweet in the context of combinatorial games, in view of their inherent high complexity.

With a slant towards artificial intelligence, Judea Pearl wrote that games “offer a perfect laboratory for studying complex problem-solving methodologies. With a few parsimonious rules, one can create complex situations that require no less insight, creativity, and expertise than problems actually encountered in areas such as business, government, scientific, legal, and others. Moreover, unlike these applied areas, games offer an arena in which computerized decisions can be evaluated by absolute standards of performance and in which proven human experts are both available and willing to work towards the goal of seeing their expertise emulated by a machine. Last, but not least, games possess addictive entertaining qualities of a very general appeal. That helps maintain a steady influx of research talents into the field and renders games a convenient media for communicating powerful ideas about general methods of strategic planning.”

To further explore the nature of games, we consider, informally, two subclasses.

(i) Games People Play (playgames): games that are challenging to the point that people will purchase them and play them.

(ii) Games Mathematicians Play (mathgames): games that are challenging to mathematicians or other scientists to play with and ponder about, but not necessarily to “the man in the street”.

Examples of playgames are chess, go, hex, reversi; of mathgames: Nim-type games, Wythoff games, annihilation games, octal games.

Some “rule of thumb” properties, which seem to hold for the majority of playgames and mathgames are listed below.

I. Complexity. Both playgames and mathgames tend to be computationally intractable. There are a few tractable mathgames, such as Nim, but most games still live in Wonderland: we are wondering about their as yet unknown complexity. Roughly speaking, however, NP-hardness is a necessary but not a sufficient condition for being a playgame! (Some games on Boolean formulas are Exptime-complete, yet none of them seems to have the potential of commercial marketability.)

II. Boardfeel. None of us may know an exact strategy from a midgame position of chess, but even a novice, merely by looking at the board, gets some feel who of the two players is in a stronger position – even what a strong or weak next move is. This is what we loosely call boardfeel. Our informal definition of playgames and mathgames suggests that the former do have a boardfeel, whereas the latter don’t. For many mathgames, such as Nim, a player without prior knowledge of the strategy has no inkling whether any given position is “strong” or “weak” for a player. Even when defeat is imminent, only one or two moves away, the player sustaining it may be in the dark about the outcome, which will startle and stump him. The player has no boardfeel. (Many mathgames, including Nim-type games, can be played, equivalently, on a board.)

Thus, in the boardfeel sense, simple games are complex and complex games are simple! This paradoxical property also doesn’t seem to have an analog in the realm of decision problems. The boardfeel is the main ingredient which makes PlayGames interesting to play.

III. Math Appeal. Playgames, in addition to being interesting to play, also have considerable mathematical appeal. This has been exposed recently by the theory of partizan games established by Conway and applied to endgames of go by Berlekamp, students and associates. On the other hand, mathgames have their own special combinatorial appeal, of a somewhat different flavor. They are created by mathematicians and appeal to them, since they experience special intellectual challenges in analyzing them. As Peter Winkler called a subset of them: “games people don’t play”. We might also call them, in a more positive vein, “games mathematicians play”. Both classes of games have applications to areas outside game theory. Examples: surreal numbers (playgames), error correcting codes (mathgames). Both provide enlightenment through bewilderment, as David Wolfe and Tom Rodgers put it.

IV. Existence. There are relatively few successful playgames around. It seems to be hard to invent a playgame that catches the masses. In contrast, mathgames abound. They appeal to a large subclass of mathematicians and other scientists, who cherish producing them and pondering about them. The large proportion of mathgames-papers in the games bibliography below reflects this phenomenon.

We conclude, inter alia, that for playgames, high complexity is desirable. Whereas in all respectable walks of life we strive towards solutions or at least approximate solutions which are polynomial, there are two “less respectable” human activities in which high complexity is savored. These are cryptography (covert warfare) and games (overt warfare). The desirability of high complexity in cryptography — at least for the encryptor! — is clear. We claim that it is also desirable for playgames.

It’s no accident that games and cryptography team up: in both there are adversaries, who pit their wits against each other! But games are, in general, considerably harder than cryptography. For the latter, the problem whether the designer of a cryptosystem has a safe system can be expressed with two quantifiers only: ∃ a cryptosystem such that ∀ attacks on it, the cryptosystem remains unbroken? In contrast, the decision problem whether White can win if White moves first in a chess game, has the form: “∃∀∃∀ ⋯ move: White wins?”, expressing the question whether White has an opening winning move — with an unbounded number of alternating quantifiers. This makes games the more challenging and fascinating of the two, besides being fun! See also the next section.

Thus, it’s no surprise that the skill of playing games, such as checkers, chess, or go has long been regarded as a distinctive mark of human intelligence.

3 Why are Combinatorial Games Hard?

Existential decision problems, such as graph hamiltonicity and Traveling Salesperson (Is there a round tour through specified cities of cost ≤ C?), involve a single existential quantifier (“Is there… ?”). In mathematical terms an existential problem boils down to finding a path—sometimes even just verifying its existence—in a large “decision-tree” of all possibilities, that satisfies specified properties. The above two problems, as well as thousands of other interesting and important combinatorial-type problems are NP-complete. This means that they are conditionally intractable, i.e., the best way to solve them seems to require traversal of most if not all of the decision tree, whose size is exponential in the input size of the problem. No essentially better method is known to date at any rate, and, roughly speaking, if an efficient solution will ever be found for any NP-complete problem, then all NP-complete problems will be solvable efficiently.

The decision problem whether White can win if White moves first in a chess game, on the other hand, has the form: Is there a move of White such that for every move of Black there is a move of White such that for every move of Black there is a move of White … such that White can win? Here we have a large number of alternating existential and universal quantifiers rather than a single existential one. We are looking for an entire subtree rather than just a path in the decision tree. Because of this, most nonpolynomial games are at least Pspace-hard. The problem for generalized chess on an n × n board, and even for a number of seemingly simpler mathgames, is, in fact, Exptime-complete, which is a provable intractability.

Put in simple language, in analyzing an instance of Traveling Salesperson, the problem itself is passive: it does not resist your attempt to attack it, yet it is difficult. In a game, in contrast, there is your opponent, who, at every step, attempts to foil your effort to win. It’s similar to the difference between an autopsy and surgery. Einstein, contemplating the nature of physics said, “Der Allmächtige ist nicht boshaft; Er ist raffiniert” (The Almighty is not mean; He is sophisticated). NP-complete existential problems are perhaps sophisticated. But your opponent in a game can be very mean!

Another manifestation of the high complexity of games is associated with a most basic tool of a game: its game-graph. It is a directed graph Γ whose vertices are the positions of the game, and (u, v) is an edge if and only if there is a move from position u to position v. As an example, consider a directed graph G with some tokens distributed on its vertices. A move consists of selecting a token on vertex w and shifting it to z if and only if (w, z) is an edge of G. Since every subset of vertices of G (those occupied by tokens) is a position of the game, and thus a single vertex in Γ, the game graph Γ of the game on G has clearly exponential size in the size of G. This kind of behavior holds, in particular, for both nim-type and chess-type games. Analyzing a game means reasoning about its game-graph. We are thus faced with a problem that is a priori exponential, quite unlike many present-day interesting existential (optimization) problems.

A fundamental notion is the sum (disjunctive compound) of games. A sum is a finite collection of disjoint games; often very basic, simple games. Each of the two players, at every turn, selects one of the games and makes a move in it. If the outcome is not a draw, the sum-game ends when there is no move left in any of the component games. If the outcome is not a tie either, then in normal play, the player first unable to move loses and the opponent wins. The outcome is reversed in misère play.

If a game decomposes into a disjoint sum of its components, either from the beginning (Nim) or after a while (domineering), the potential for its tractability increases despite the exponential size of the game graph. As Elwyn Berlekamp remarked, the situation is similar to that in other scientific endeavors, where we often attempt to decompose a given system into its functional components. This approach may yield improved insights into hardware, software or biological systems, human organizations, and abstract mathematical objects such as groups.

If a game doesn’t decompose into a sum of disjoint components, it is more likely to be intractable (Geography or Poset Games). Intermediate cases happen when the components are not quite fixed (which explains why misère play of sums of games is much harder than normal play) or not quite disjoint (Welter). Thane Plambeck and Aaron Siegel have recently revolutionized the theory of misère play, as reflected in the bibliography below.

The hardness of games is eased somewhat by the efficient freeware package “Combinatorial Game Suite”, courtesy of Aaron Siegel.

4 Breaking the Rules

As the experts know, some of the most exciting games are obtained by breaking some of the rules for combinatorial games, such as permitting a player to pass a bounded or unbounded number of times, i.e., relaxing the requirement that players play alternately; or permitting a number of players other than two.

But permitting a payoff function other than (0,1) for the outcome (lose, win) and a payoff of (\frac{1}{2}, \frac{1}{2}) for either (tie, tie) or (draw, draw) usually, but not always, leads to classical games that are not combinatorial but undetermined, notably games with applications in economics. Bernhard von Stengel has recently initiated an important effort to establish a bridge between these and combinatorial games. Though there are a few individuals who work in both disciplines, an organic connection between the two disciplines has yet to be established.

5 Why Is the Bibliography Vast?

In the realm of existential problems, such as sorting or Traveling Salesperson, most present-day interesting decision problems can be classified into tractable, conditionally intractable, and provably intractable ones. There are exceptions, to be sure, such as graph isomorphism (are two graphs isomorphic?), whose complexity is still unknown. But the exceptions are very few. In contrast, most games are still in Wonderland, as pointed out in section 2(I) above. Only a few games have been classified into the complexity classes they belong to. Despite recent impressive progress, the tools for reducing Wonderland are still few and inadequate.

To give an example, many interesting games have a very succinct input size, so a polynomial strategy is often more difficult to come by (Richard Guy and Cedric Smith’s octal games; Grundy’s game). Succinctness and non-disjointness of games in a sum may be present simultaneously (Poset games). In general, the alternating quantifiers, and, to a smaller measure, “breaking the rules”, add to the volume of Wonderland. We suspect that the large size of Wonderland, a fact of independent interest, is the main contributing factor to the bulk of the bibliography on games.

6 Why Isn’t it Larger?

The bibliography below is a partial list of books and articles on combinatorial games and related material. It is partial not only because I constantly learn of additional relevant material I did not know about previously, but also because of certain self-imposed restrictions. The most important of these is that only papers with some original and nontrivial mathematical content are considered. This excludes most historical reviews of games and most, but not all, of the work on heuristic or artificial intelligence approaches to games, especially the large literature concerning computer chess. I have, however, included the compendium edited by David Levy [2009], which, with its extensive bibliography, can serve as a first guide to this world. Also some papers on chess-endgames and clever exhaustive computer searches of some games have been included.

On the other hand, papers on games that break some of the rules of combinatorial games are included liberally, as long as they are interesting and retain a combinatorial flavor. These are vague and hard to define criteria, yet combinatorialists usually recognize a combinatorial game when they see it. Besides, it is interesting to break also this rule sometimes! We have included some references to one-player games, e.g., towers of Hanoi, n-queen problems, 15-puzzle, peg-solitaire, pebbling and others, but only few zero-player games (such as Life and some games on “sand piles”). We have also included papers on various applications of games, especially when the connection to games is substantial or the application is interesting or important.

7 Meetings and Publications

Conferences on combinatorial games, such as an AMS short course in Columbus, OH (1990), workshops at MSRI (1994, 2000), at BIRS (2005, 2011) resulted in books, or a special issue of a journal – the latter for the Dagstuhl seminar (2002). During 1990–2001, Theoretical Computer Science ran a special Mathematical Games Section whose main purpose was to publish papers on combinatorial games. TCS still solicits papers on games. In 2002, Integers—Electronic J. of Combinatorial Number Theory began publishing a Combinatorial Games Section. The combinatorial games community is growing in quantity and quality! In 2011 the “Game Theory Society” (classical games) posted on its web site http://www.gametheorysociety.org/ a call for papers inviting submissions of high-class papers in combinatorial game theory for its flagship publication Intern. J. Game Theory. The first few submissions are in the refereeing process, some already accepted.

8 The Dynamics of the Bibliography

The game bibliography below is very dynamic in nature. Previous versions have been circulated to colleagues, intermittently, since the early 1980’s (surface mail!). Prior to every mailing updates were prepared, and usually also afterwards, as a result of the comments received from several correspondents. Naturally, the listing can never be “complete”. Thus also the present form of the bibliography is by no means complete.

Because of its dynamic nature, it is natural that the bibliography became a “Dynamic Survey” in the Dynamic Surveys (DS) section of the Electronic Journal of Combinatorics (ElJC) http://www.combinatorics.org/ (click on “Surveys”). The ElJC has mirrors at various locations. Furthermore, the European Mathematical Information Service (EMIS) mirrors this Journal, as do all of its mirror sites (currently forty of them). See http://www.emis.de/tech/mirrors/index.html

9 An Appeal

I ask readers to continue sending to me corrections and comments; and inform me of significant omissions, remembering, however, that it is a selected bibliography. I prefer to get reprints, preprints or URLs, rather than only titles — whenever possible.

Material on games is mushrooming on the Web. The URLs can be located using a standard search engine, such as Google.

10 Idiosyncrasies

Most of the bibliographic entries refer to items written in English, though there is a sprinkling of Danish, Dutch, French, German, Japanese, Slovakian and Russian, as well as some English translations from Russian. The predominance of English may be due to certain prejudices, but it also reflects the fact that nowadays the lingua franca of science is English. In any case, I’m soliciting also papers in languages other than English, especially if accompanied by an abstract in English.

On the administrative side, Technical Reports, submitted papers and unpublished theses have normally been excluded; but some exceptions have been made. Abbreviations of book series and journal names usually follow the Math Reviews conventions. Another convention is that de Bruijn appears under D, not B; von Neumann under V, not N, McIntyre under M not I, etc.

Earlier versions of this bibliography have appeared, under the title “Selected bibliography on combinatorial games and some related material”, as the master bibliography for the book Combinatorial Games, AMS Short Course Lecture Notes, Summer 1990, Ohio State University, Columbus, OH, Proc. Symp. Appl. Math. 43 (R. K. Guy, ed.), AMS 1991 with 400 items; and in the Dynamic Surveys section of the Electronic J. of Combinatorics in November 1994 with 542 items, updated there at odd times. It also appeared as the master bibliography in Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA (R. J. Nowakowski, ed.), MSRI Publ. Vol. 29, Cambridge University Press, Cambridge, 1996, under the present title, containing 666 items. The version published in the palindromic year 2002 contained the palindromic number 919 of references (More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, R. J. Nowakowski, ed., MSRI Publ. Vol. 42, Cambridge University Press, Cambridge. In GONC 3 (Games Of No Chance) it contained 1360 items, and the present version, to be published in GONC 4, contains 1700 items.

11 Acknowledgments

Many people have suggested additions to the bibliography, or contributed to it in other ways. Ilan Vardi distilled my Math-master (§2) into Mathter. Among those that contributed more than two or three items are: Akeo Adachi, Ingo Althöfer, Thomas Andreae, Eli Bachmupsky, the late Adriano Barlotti, József Beck, the late Claude Berge, Gerald E. Bergum, the late H. S. MacDonald Coxeter, Thomas S. Ferguson, James A. Flanigan, Fred Galvin, Martin Gardner, Alan J. Goldman, Solomon W. Golomb, Richard K. Guy, Shigeki Iwata, David S. Johnson, Victor Klee, Donald E. Knuth, the late Anton Kotzig, Jeff C. Lagarias, Michel Las Vergnas, Hendrik W. Lenstra, Hermann Loimer, F. Lockwood Morris, Richard J. Nowakowski, Judea Pearl, J. Michael Robson, David Singmaster, Wolfgang Slany, Cedric A. B. Smith, Rastislaw Telgársky, Mark D. Ward, Yōhei Yamasaki and others. Thanks to all and keep up the game! Special thanks to Mark Ward who went through the entire file with a fine comb in late 2005, when it contained 1,151 items, correcting errors and typos. Many thanks also to various anonymous helpers who assisted with the initial TEX file, to Silvio Levy, who has edited and transformed it into L^{A}TEX2e in 1996, and to Wolfgang Slany, who has transformed it into a BIBTeX file at the end of the previous millenium, and solved a “new millenium” problem encountered when the bibliography grew beyond 999 items. Keen users of the bibliography will notice that there is a beginning of MR references, due to Richard Guy’s suggestion, facilitated by his former student Alex Fink. I have learned from Kevin O’Bryant’s paper “Fraenkel’s partition and Brown’s decomposition”, Integers 3 (2003), A11, 17 pp., that Lord Rayleigh had anticipated the so-called ‘Beatty’s Theorem” many years before Beatty, but without proof. See the Rayleigh and Beatty entries below.

12 The Bibliography

1. S. Abbasi and N. Sheikh [2007], Some hardness results for question/answer games, Integers, Electr. J of Combinat. Number Theory 7, #G08, 29 pp., MR2342186.

     http://www.integers-ejcnt.org/vol7.html

2. S. Abbasi and N. Sheikh [2008], Complexity of question/answer games, Theoret. Comput. Sci. 409, 364–381, 2473911 (2010i:68049).

     http://dx.doi.org/10.1016/j.tcs.2008.08.034

3. S. Abbasi and N. Sheikh [2008], Question/answer games on towers and pyramids, in: Mathematical foundations of computer science 2008 , Vol. 5162 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 83–95, 2539361 (2011c:68157).

     http://dx.doi.org/10.1007/978-3-540-85238-4_6

4. L. Abrams and D. S. Cowen-Morton [2010], Algebraic structure in a family of Nim-like arrays, J. Pure Appl. Algebra 214(2), 165–176, 2559688 (2011c:20129).

     http://dx.doi.org/10.1016/j.jpaa.2009.05.015

5. L. Abrams and D. S. Cowen-Morton [2010], Periodicity and other structure in a colorful family of Nim-like arrays, Electron. J. Combin.

17(1), Research Paper 103, 21, 2679557 (2012a:91046).

http://www.combinatorics.org/Volume_17/Abstracts/v17i1r103.
html

6. B. Abramson and M. Yung [1989], Divide and conquer under global constraints: a solution to the n-queens problem, J. Parallel Distrib. Comput. 6, 649–662.

7. A. Adachi, S. Iwata and T. Kasai [1981], Low level complexity for combinatorial games, Proc. 13th Ann. ACM Symp. Theory of Computing (Milwaukee, WI, 1981), Assoc. Comput. Mach., New York, NY, pp. 228–237.

8. A. Adachi, S. Iwata and T. Kasai [1984], Some combinatorial game problems require Ω(n^{k}) time, J. Assoc. Comput. Mach. 31(2), 361–376, 819145.

http://dx.doi.org/10.1145/62.322433

9. H. Adachi, H. Kamekawa and S. Iwata [1987], Shogi on n × n board is complete in exponential time, Trans. IEICE J70-D, 1843–1852 (in Japanese).

10. E. W. Adams and D. C. Benson [1956], Nim-Type Games, Technical Report No. 31 , Department of Mathematics, Pittsburgh, PA.

11. W. Ahrens [1910], Mathematische Unterhaltungen und Spiele, Vol. I, Teubner, Leipzig, Zweite vermehrte und verbesserte Auflage. (There are further editions and related game-books of Ahrens).

12. O. Aichholzer, D. Bremner, E. D. Demaine, F. Hurtado, E. Kranakis, H. Krasser, S. Ramaswami, S. Sethia and J. Urrutia [2005], Games on triangulations, Theoret. Comput. Sci. 343(1-2), 42–71, 2168844 (2006d:91037).

http://dx.doi.org/10.1016/j.tcs.2005.05.007

13. S. Aida, M. Crasmaru, K. Regan and O. Watanabe [2004], Games with uniqueness properties, Theory Comput. Syst. 37, 29–47, Symposium on Theoretical Aspects of Computer Science (Antibes-Juan les Pins, 2002), MR2038401 (2004m:68055).

14. M. Aigner [1995], Ulams Millionenspiel, Math. Semesterber. 42, 71–80.

15. M. Aigner [1996], Searching with lies, J. Combin. Theory (Ser. A) 74, 43–56.

16. M. Aigner and M. Fromme [1984], A game of cops and robbers, Discrete Appl. Math. 8, 1–11, MR739593 (85f:90124).

17. M. Ajtai, L. Csirmaz and Z. Nagy [1979], On a generalization of the game Go-Moku I, Studia Sci. Math. Hungar. 14, 209–226.

18. E. Akin and M. Davis [1985], Bulgarian solitaire, Amer. Math. Monthly 92, 237–250, MR786523 (86m:05014).

19. D. J. Albers and G. L. Alexanderson [1993], A conversation with Richard Guy, College Math. J. 24, 123–148.

20. M. H. Albert, R. E. L. Aldred, M. D. Atkinson, C. C. Handley, D. A. Holton, D. J. McCaughan and B. E. Sagan [2008], Monotonic sequence games, in: Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 309–327.

21. M. H. Albert, J. P. Grossman, R. J. Nowakowski and D. Wolfe [2005], An introduction to clobber, Integers 5(2), A1, 12, 2192079 (2006k:91055).

22. M. H. Albert and R. J. Nowakowski [2001], The game of End-Nim, Electron. J. Combin. 8(2), Research Paper 1, 12 pp. (electronic), In honor of Aviezri Fraenkel on the occasion of his 70th birthday, 1853252 (2002g:91044).

http://www.combinatorics.org/Volume_8/Abstracts/v8i2r1.html

23. M. H. Albert and R. J. Nowakowski [2004], NIM restrictions, Integers 4, G1, 10, 2056015.

24. M. H. Albert and R. J. Nowakowski [2011], Lattices of games, Order 16, 1–10.

25. M. Albert, R. J. Nowakowski and D. Wolfe [2007], Lessons in Play: An Introduction to Combinatorial Game Theory, A K Peters, Wellesley, MA.

26. R. E. Allardice and A. Y. Fraser [1884], La tour d’Hanoï, Proc. Edinburgh Math. Soc. 2, 50–53.

27. D. T. Allemang [1984], Machine computation with finite games, M.Sc. Thesis, Cambridge University.

28. D. T. Allemang [2001], Generalized genus sequences for misère octal games, Internat. J. Game Theory 30(4), 539–556 (2002), 1907264 (2003h:91003).

http://dx.doi.org/10.1007/s001820200097

29. J. D. Allen [1989], A note on the computer solution of Connect-Four, Heuristic Programming in Artificial Intelligence 1: The First Computer Olympiad (D. N. L. Levy and D. F. Beal, eds.), Ellis Horwood, Chichester, England, pp. 134–135.

30. M. R. Allen [2007], On the periodicity of genus sequences of quaternary games, Integers, Electr. J. of Combinat. Number Theory 7, #G04, 11 pp., MR2299810 (2007k:91050).

http://www.integers-ejcnt.org/vol7.html

31. N. L. Alling [1985], Conway’s field of surreal numbers, Trans. Amer. Math. Soc. 287, 365–386.

32. N. L. Alling [1987], Foundations of Analysis Over Surreal Number Fields, North-Holland, Amsterdam.

33. N. L. Alling [1989], Fundamentals of analysis over surreal number fields, Rocky Mountain J. Math. 19, 565–573.

34. N. L. Alling and P. Ehrlich [1986], An abstract characterization of a full class of surreal numbers, C. R. Math. Rep. Acad. Sci. 8, 303–308.

35. N. L. Alling and P. Ehrlich [1986], An alternative construction of Conway’s surreal numbers, C. R. Math. Rep. Acad. Sci. 8, 241–246.

36. L. V. Allis [1994], Searching for solutions in games and artificial intelligence, Ph.D. Thesis, University of Limburg.

ftp://ftp.cs.vu.nl/pub/victor/PhDthesis/thesis.ps.Z

37. L. V. Allis and P. N. A. Schoo [1992], Qubic solved again, Heuristic Programming in Artificial Intelligence 3: The Third Computer Olympiad (H. J. van den Herik and L. V. Allis, eds.), Ellis Horwood, New York, pp. 192–204.

38. L. V. Allis, H. J. van den Herik and M. P. H. Huntjens [1993], Go-Moku solved by new search techniques, Proc. 1993 AAAI Fall Symp. on Games: Planning and Learning, AAAI Press Tech. Report FS93–02, Menlo Park, CA, pp. 1–9.

39. J.-P. Allouche, D. Astoorian, J. Randall and J. Shallit [1994], Morphisms, squarefree strings, and the tower of Hanoi puzzle, Amer. Math. Monthly 101, 651–658, MR1289274 (95g:68090).

40. J.-P. Allouche and A. Sapir [2005], Restricted towers of Hanoi and morphisms, in: Developments in Language Theory, Vol. 3572 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 1–10, MR2187246 (2006g:68266).

41. N. Alon, J. Balogh, B. Bollobás and T. Szabó [2002], Game domination number, Discrete Math. 256, 23–33, MR1927054 (2003f:05086).

42. N. Alon, M. Krivelevich, J. Spencer and T. Szabó [2005], Discrepancy games, Electr. J. Combin. 12(1), #R51, 9 pp., MR2176527.

http://www.combinatorics.org/

43. N. Alon and A. Mehrabian [2011], On a generalization of Meyniel’s conjecture on the Cops and Robbers game, Electron. J. Combin. 18(1), Paper 19, 7, 2770124 (2012c:05205).

44. N. Alon and Z. Tuza [1995], The acyclic orientation game on random graphs, Random Structures Algorithms 6, 261–268.

45. S. Alpern and A. Beck [1991], Hex games and twist maps on the annulus, Amer. Math. Monthly 98, 803–811.

46. B. Alspach [2004], Searching and sweeping graphs: a brief survey, Matematiche (Catania) 59(1-2), 5–37 (2006), 2243023 (2008e:05061).

47. I. Althöfer [1988], Nim games with arbitrary periodic moving orders, Internat. J. Game Theory 17, 165–175.

48. I. Althöfer [1988], On the complexity of searching game trees and other recursion trees, J. Algorithms 9, 538–567.

49. I. Althöfer [1989], Generalized minimax algorithms are no better error correctors than minimax is itself, in: Advances in Computer Chess (D. F. Beal, ed.), Vol. 5, Elsevier, Amsterdam, pp. 265–282.

50. I. Althöfer [1994], On sparse approximations to randomized strategies and convex combinations, Linear Algebra Appl. 199, 339–355, 1274423 (95m:90156).

http://dx.doi.org/10.1016/0024-3795(94)90357-3

51. I. Althöfer and J. Bültermann [1995], Superlinear period lengths in some subtraction games, Theoret. Comput. Sci. (Math Games) 148, 111–119.

52. G. Ambrus and J. Barát [2006], A contribution to queens graphs: a substitution method, Discrete Math. 306(12), 1105–1114, MR2245636

(2007b:05174).

53. M. Anderson and T. Feil [1998], Turning lights out with linear algebra, Math. Mag. 71, 300–303.

54. M. Anderson and F. Harary [1987], Achievement and avoidance games for generating abelian groups, Internat. J. Game Theory 16, 321–325.

55. R. Anderson, L. Lovász, P. Shor, J. Spencer, É. Tardos and S. Winograd [1989], Disks, balls, and walls: analysis of a combinatorial game, Amer. Math. Monthly 96(6), 481–493, 999411 (90e:90169).

http://dx.doi.org/10.2307/2323970

56. W. N. Anderson, Jr. [1974], Maximum matching and the game of Slither, J. Combinatorial Theory Ser. B 17, 234–239, 0364014 (51 #269).

57. T. Andreae [1984], Note on a pursuit game played on graphs, Discrete Appl. Math. 9, 111–115.

58. T. Andreae [1986], On a pursuit game played on graphs for which a minor is excluded, J. Combin. Theory Ser. B 41(1), 37–47, 854602 (87i:05179).

http://dx.doi.org/10.1016/0095-8956(86)90026-2

59. T. Andreae, F. Hartenstein and A. Wolter [1999], A two-person game on graphs where each player tries to encircle his opponent’s men, Theoret. Comput. Sci. (Math Games) 215, 305–323.

60. V. Andrejić [2009], On a combinatorial game, Publ. Inst. Math. (Beograd) (N.S.) 86(100), 21–25, 2567763 (2011a:91085).

http://dx.doi.org/10.2298/PIM0900021A

61. S. D. Andres [2003], The game chromatic index of forests of maximum degree 5, in: 2nd Cologne-Twente Workshop on Graphs and Combinatorial Optimization, Vol. 13 of Electron. Notes Discrete Math., Elsevier, Amsterdam, p. 4 pp. (electronic), MR2153344.

62. S. D. Andres [2006], Game-perfect graphs with clique number 2, in: CTW2006—Cologne-Twente Workshop on Graphs and Combinatorial Optimization, Vol. 25 of Electron. Notes Discrete Math., Elsevier, Amsterdam, pp. 13–16 (electronic), MR2301125 (2008a:05080).

63. S. D. Andres [2006], The game chromatic index of forests of maximum degree Δ ≥ 5, Discrete Appl. Math. 154(9), 1317–1323, 2221551 (2007b:05066).

http://dx.doi.org/10.1016/j.dam.2005.05.031

64. S. D. Andres [2009], Asymmetric directed graph coloring games, Discrete Math. 309(18), 5799–5802, 2567985 (2010m:05194).

http://dx.doi.org/10.1016/j.disc.2008.03.022

65. S. D. Andres [2009], Game-perfect graphs, Math. Methods Oper. Res. 69(2), 235–250, 2491810 (2011a:05124).

http://dx.doi.org/10.1007/s00186-008-0256-3

66. S. D. Andres [2009], Lightness of digraphs in surfaces and directed game chromatic number, Discrete Math. 309(11), 3564–3579, 2528070 (2011a:05126).

http://dx.doi.org/10.1016/j.disc.2007.12.060

67. S. D. Andres [2009], The incidence game chromatic number, Discrete Appl. Math. 157(9), 1980–1987, 2522464 (2010i:05108).

http://dx.doi.org/10.1016/j.dam.2007.10.021

68. S. D. Andres [2010], Directed defective asymmetric graph coloring games, Discrete Appl. Math. 158, 251–260, 2588109 (2011c:05223).

http://dx.doi.org/10.1016/j.dam.2009.04.025

69. S. D. Andres [2010], Erratum to: The incidence game chromatic number [Discrete Appl. Math. 157 (9) (2009) 1980–1987] [MR2522464], Discrete Appl. Math. 158(6), 728, 2594489 (2011c:05120).

http://dx.doi.org/10.1016/j.dam.2009.11.017

70. S. D. Andres [2010], Note on the number of rooted complete N-ary trees, Ars Combin. 94, 465–469, 2599757 (2010m:05150).

71. S. D. Andres and W. Hochstättler [2011], The game chromatic number and the game colouring number of classes of oriented cactuses, Inform. Process. Lett. 111(5), 222–226, 2790744 (2012b:05109).

http://dx.doi.org/10.1016/j.ipl.2010.11.020

72. S. D. Andres, W. Hochstättler and C. Schallück [2011], The game chromatic index of wheels, Discrete Appl. Math. 159(16), 1660–1665, 2825608.

http://dx.doi.org/10.1016/j.dam.2010.05.003

73. V. V. Anshelevich [2000], The Game of Hex: an automatic theorem proving approach to game programming, Proc. 17-th National Conference on Artificial Intelligence (AAAI-2000), AAAI Press, Menlo Park, CA, pp. 189–194, MR1973011 (2004b:91039).

74. V. V. Anshelevich [2002], The game of Hex: the hierarchical approach, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 151–165.

75. R. P. Anstee and M. Farber [1988], On bridged graphs and cop-win graphs, J. Combin. Theory (Ser. B) 44, 22–28.

76. A. Apartsin, E. Ferapontova and V. Gurvich [1998], A circular graph— counterexample to the Duchet kernel conjecture, Discrete Math. 178, 229–231, MR1483752 (98f:05122).

77. D. Applegate, G. Jacobson and D. Sleator [1999], Computer analysis of Sprouts, in: The Mathemagician and Pied Puzzler, honoring Martin Gardner; E. Berlekamp and T. Rodgers, eds., A K Peters, Natick, MA, pp. 199-201.

78. A. A. Arakelyan [1982], D-products and compositions of Nim games, Akad. Nauk Armyan. SSR Dokl. 74, 3–6, (Russian).

79. J. C. S. Araújo and C. L. Sales [2009], Grundy number of P_{4}-classes, in: LAGOS’09—V Latin-American Algorithms, Graphs and Optimization Symposium, Vol. 35 of Electron. Notes Discrete Math., Elsevier Sci. B. V., Amsterdam, pp. 21–27, 2579402.

http://dx.doi.org/10.1016/j.endm.2009.11.005

80. S. Aravamuthan and S. Lodha [2006], Covering codes for Hats-on-a-line, Electron. J. Combin. 13, Research Paper 21, 12 pp. (electronic), MR2212494 (2006j:91072).

http://www.combinatorics.org/Volume_13/Abstracts/v13i1r21.
html

81. A. F. Archer [1999], A modern treatment of the 15 puzzle, Amer. Math. Monthly 106, 793–799.

82. P. Arnold, ed. [1993], The Book of Games, Hamlyn, Chancellor Press.

83. A. A. Arratia-Quesada and I. A. Stewart [1997], Generalized Hex and logical characterizations of polynomial space, Inform. Process. Lett. 63, 147–152.

84. A. A. Arratia and I. A. Stewart [2003], A note on first-order projections and games, Theoret. Comput. Sci. 290, 2085–2093, MR1937766 (2003i:68034).

85. M. Ascher [1987], Mu Torere: An analysis of a Maori game, Math. Mag. 60, 90–100.

86. I. M. Asel’derova [1974], On a certain discrete pursuit game on graphs, Cybernetics 10, 859–864, trans. of Kibernetika 10 (1974) 102–105.

87. J. A. Aslam and A. Dhagat [1993], On-line algorithms for 2-coloring hypergraphs via chip games, Theoret. Comput. Sci. (Math Games) 112, 355–369.

88. M. Asté, F. Havet and C. Linhares-Sales [2010], Grundy number and products of graphs, Discrete Math. 310(9), 1482–1490, 2601252 (2011g:05090).

http://dx.doi.org/10.1016/j.disc.2009.09.020

89. M. D. Atkinson [1981], The cyclic towers of Hanoi, Inform. Process. Lett. 13, 118–119.

90. J. M. Auger [1991], An infiltration game on k arcs, Naval Res. Logistics 38, 511–529.

91. V. Auletta, A. Negro and G. Parlati [1992], Some results on searching with lies, Proc. 4th Italian Conf. on Theoretical Computer Science, L’Aquila, Italy, pp. 24–37.

92. J. Auslander, A. T. Benjamin and D. S. Wilkerson [1993], Optimal leapfrogging, Math. Mag. 66, 14–19.

93. R. Austin [1976], Impartial and partisan games, M.Sc. Thesis, Univ. of Calgary.

94. D. Avis and A. Deza [2001], On the binary solitaire cone, Discrete Appl. Math. 115(1-3), 3–14, 1st Japanese-Hungarian Symposium for Discrete Mathematics and its Applications (Kyoto, 1999), 1869344 (2002i:05016).

http://dx.doi.org/10.1016/S0166-218X(01)00211-6

95. D. Avis and A. Deza [2001], On the solitaire cone and its relationship to multi-commodity flows, Math. Program. 90(1, Ser. A), 27–57, 1819785 (2002c:91033).

http://dx.doi.org/10.1007/PL00011419

96. J. O. A. Ayeni and H. O. D. Longe [1985], Game people play: Ayo, Internat. J. Game Theory 14, 207–218.

97. D. Azriel and D. Berend [2006], On a question of Leiss regarding the Hanoi Tower problem, Theoret. Comput. Sci. 369(1-3), 377–383, MR2277583 (2007h:68226).

98. L. Babai [1985], Trading group theory for randomness, Proc. 17th Ann. ACM Symp. Theory of Computing, Assoc. Comput. Mach., New York, NY, pp. 421 – 429.

99. L. Babai and S. Moran [1988], Arthur–Merlin games: a randomized proof system, and a hierarchy of complexity classes, J. Comput. System Sci. 36, 254–276.

100. R. J. R. Back and J. von Wright [1995], Games and winning strategies, Inform. Process. Lett. 53, 165–172.

101. R. Backhouse and D. Michaelis [2004], Fixed-point characterisation of winning strategies in impartial games in: Relational and Kleene-Algebraic Methods in Computer Science, Vol. 3051/2004, Lecture Notes in Computer Scienc, Springer Berlin, Heidelberg, pp. 34–47.

102. F. Bagemihl [1956], Transfinitely endless chess, Z. Math. Logik Grundlagen Math. 2, 215–217, 0083934 (18,783e).

103. C. K. Bailey [1986], A combinatorial card game, Proceedings of the seventeenth Southeastern international conference on combinatorics, graph theory, and computing (Boca Raton, Fla., 1986), Vol. 53, pp. 75–78, 885236 (88c:05007).

104. C. K. Bailey and M. E. Kidwell [1985], A king’s tour of the chessboard, Math. Mag. 58, 285–286.

105. R. Balakrishnan and T. Kavaskar [2013], Interpolation theorem for partial Grundy coloring, Discrete Math. 313(8), 949–950, 3021504.

http://dx.doi.org/10.1016/j.disc.2013.01.018

106. W. W. R. Ball and H. S. M. Coxeter [1987], Mathematical Recreations and Essays, Dover, New York, NY, 13th edn.

107. B. A. Balof and J. J. Watkins [1996], Knight’s tours and magic squares, Congr. Numer. 120, 23–32, Proc. 27th Southeastern Internat. Conf. on Combinatorics, Graph Theory and Computing (Baton Rouge, LA, 1996), MR1431952.

108. J. Balogh and W. Samotij [2011], On the Chvátal-Erdős triangle game, Electron. J. Combin. 18(1), Paper 72, 15, 2788689 (2012c:05206).

109. B. Banaschewski and A. Pultr [1990/91], Tarski’s fixpoint lemma and combinatorial games, Order 7(4), 375–386, 1120984 (92f:90090).

http://dx.doi.org/10.1007/BF00383202

110. R. B. Banerji [1971], Similarities in games and their use in strategy construction, Proc. Symp. Computers and Automata (J. Fox, ed.), Polytechnic Press, Brooklyn, NY, pp. 337–357.

111. R. B. Banerji [1980], Artificial Intelligence, A Theoretical Approach, Elsevier, North-Holland, New York, NY.

112. R. B. Banerji and C. A. Dunning [1992], On misere games, Cybernetics and Systems 23, 221–228.

113. R. B. Banerji and G. W. Ernst [1972], Strategy construction using homomorphisms between games, Artificial Intelligence 3, 223–249.

114. R. Bar Yehuda, T. Etzion and S. Moran [1993], Rotating-table games and derivatives of words, Theoret. Comput. Sci. (Math Games) 108, 311–329.

115. A. Barabash, A. S. Fraenkel and B. Weiss [1992/93], Iterated Beatty functions, Random Comput. Dynam. 1, 333–348, MR1214102 (94g:11010).

116. I. Bárány [1979], On a class of balancing games, J. Combin. Theory Ser. A 26(2), 115–126, 530283 (81a:90159).

http://dx.doi.org/10.1016/0097-3165(79)90061-X

117. J. Barát and M. Stojaković [2010], On winning fast in avoider-enforcer games, Electron. J. Combin. 17(1), Research Paper 56, 12, 2644843 (2011d:91058).

http://www.combinatorics.org/Volume_17/Abstracts/v17i1r56.
html

118. J. G. Baron [1974], The game of nim — a heuristic approach, Math. Mag. 47, 23–28.

119. T. Bartnicki, B. Brešar, J. Grytczuk, M. Kovše, Z. Miechowicz and I. Peterin [2008], Game chromatic number of Cartesian product graphs, Electron. J. Combin. 15(1), Research Paper 72, 13, MR2411449 (2009c:05069).

http://www.combinatorics.org/Volume_15/Abstracts/v15i1r72.
html

120. T. Bartnicki, J. A. Grytczuk and H. A. Kierstead [2008], The game of arboricity, Discrete Math. 308(8), 1388–1393, MR2392056 (2008m:05094).

http://dx.doi.org/10.1016/j.disc.2007.07.066

121. T. Bartnicki, J. Grytczuk, H. A. Kierstead and X. Zhu [2007], The mapcoloring game, Amer. Math. Monthly 114, 793–803, MR2360907.

122. R. Barua and S. Ramakrishnan [1996], σ-game, σ^{+}-game and two-dimen-sional additive cellular automata, Theoret. Comput. Sci. (Math Games) 154, 349–366.

123. V. J. D. Baston and F. A. Bostock [1985], A game locating a needle in a cirular haystack, J. Optimization Theory and Applications 47, 383–391.

124. V. J. D. Baston and F. A. Bostock [1986], A game locating a needle in a square haystack, J. Optimization Theory and Applications 51, 405–419.

125. V. J. D. Baston and F. A. Bostock [1987], Discrete hamstrung squad car games, Internat. J. Game Theory 16, 253–261.

126. V. J. D. Baston and F. A. Bostock [1988], A simple cover-up game, Amer. Math. Monthly 95, 850–854.

127. V. J. D. Baston and F. A. Bostock [1989], A one-dimensional helicoptersubmarine game, Naval Res. Logistics 36, 479–490.

128. V. J. D. Baston and F. A. Bostock [1993], Infinite deterministic graphical games, SIAM J. Control Optim. 31, 1623–1629.

129. J. Baumgartner, F. Galvin, R. Laver and R. McKenzie [1975], Game theoretic versions of partition relations, in: Colloquia Mathematica Societatis János Bolyai 10, Proc. Internat. Colloq. on Infinite and Finite Sets, Vol. 1, Keszthely, Hungary, 1973 (A. Hajnal, R. Rado and V. T. Sós, eds.), North-Holland, pp. 131–135.

130. J. D. Beasley [1985], The Ins & Outs of Peg Solitaire, Oxford University Press, Oxford.

131. J. D. Beasley [1989], The Mathematics of Games, Oxford University Press, Oxford.

132. S. Beatty [1926], Problem 3173, Amer. Math. Monthly 33, 159, Solution [to Problem 3177, numbering in 33 was erroneous] in 34 (1927) 159-160.

133. L. Beaudou, E. Duchêne and S. Gravier [2013], A survey about Solitaire Clobber, in: Games of No Chance 4 , Cambridge University Press, to appear.

134. P. Beaver [1995], Victorian Parlour Games, Magna Books.

135. A. Beck [1969], Games, in: Excursions into Mathematics (A. Beck, M. N. Bleicher and D. W. Crowe, eds.), A K Peters, Natick, MA, millennium edn., Chap. 5, pp. 317–387, With a foreword by Martin Gardner; first appeared in 1969, Worth Publ., MR1744676 (2000k:00002).

136. J. Beck [1981], On positional games, J. Combin. Theory (Ser. A) 30, 117–133.

137. J. Beck [1981], Van der Waerden and Ramsey type games, Combinatorica 1, 103–116.

138. J. Beck [1982], On a generalization of Kaplansky’s game, Discrete Math. 42, 27–35.

139. J. Beck [1982], Remarks on positional games, I, Acta Math. Acad. Sci. Hungar. 40(1–2), 65–71.

140. J. Beck [1983], Biased Ramsey type games, Studia Sci. Math. Hung. 18, 287–292.

141. J. Beck [1985], Random graphs and positional games on the complete graph, Ann. Discrete Math. 28, 7–13.

142. J. Beck [1993], Achievement games and the probabilistic method, in: Combinatorics, Paul Erdős is Eighty, Vol. 1, Bolyai Soc. Math. Stud., János Bolyai Math. Soc., Budapest, pp. 51–78.

143. J. Beck [1994], Deterministic graph games and a probabilistic intuition, Combin. Probab. Comput. 3, 13–26.

144. J. Beck [1996], Foundations of positional games, Random Structures Algorithms 9, 15–47, appeared first in: Proc. Seventh International Conference on Random Structures and Algorithms, Atlanta, GA, 1995.

145. J. Beck [1997], Games, randomness and algorithms, in: The Mathematics of Paul Erdős (R. L. Graham and J. Nešetřil, eds.), Vol. I, Springer, pp. 280–310.

146. J. Beck [1997], Graph games, Proc. Int. Coll. Extremal Graph Theory, Balatonlelle, Hungary.

147. J. Beck [2002], Positional games and the second moment method, Combinatorica 22, 169–216, special issue: Paul Erdös and his mathematics, MR1909083 (2003i:91027).

148. J. Beck [2002], Ramsey games, Discrete Math. 249, 3–30, MR1898254 (2003e:05084).

149. J. Beck [2002], The Erdös-Selfridge theorem in positional game theory, Bolyai Soc. Math. Stud. 11, 33–77, Paul Erdös and his mathematics, II, János Bolyai Math. Soc., Budapest, MR1954724 (2004a:91028).

150. J. Beck [2002], Tic-Tac-Toe, Bolyai Soc. Math. Stud. 10, 93–137, János Bolyai Math. Soc., Budapest, MR1919569 (2003e:05137).

151. J. Beck [2005], Positional games, Combin. Probab. Comput. 14(5-6), 649– 696, MR2174650 (2006f:91030).

152. J. Beck [2008], Combinatorial games: Tic-tac-toe theory, Vol. 114 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, MR2402857 (2009g:91038).

153. J. Beck and L. Csirmaz [1982], Variations on a game, J. Combin. Theory (Ser. A) 33, 297–315.

154. R. A. Beeler, A. D. Gray and D. P. Hoilman [2012], Constructing solvable graphs in peg solitaire, Bull. Inst. Combin. Appl. 66, 89–96.

155. R. A. Beeler and D. Paul Hoilman [2011], Peg solitaire on graphs, Discrete Math. 311(20), 2198–2202, 2825664.

http://dx.doi.org/10.1016/j.disc.2011.07.006

156. R. Beigel and W. I. Gasarch [1991], The mapmaker’s dilemma, Discrete Appl. Math. 34, 37–48.

157. L. W. Beineke, I. Broereand and M. A. Henning [1999], Queens graphs, Discrete Math. 206, 63–75, Combinatorics and number theory (Tiruchirappalli, 1996), MR1665386 (2000f:05066).

158. A. Bekmetjev, G. Brightwell, A. Czygrinow and G. Hurlbert [2003], Thresholds for families of multisets, with an application to graph pebbling, Discrete Math. 269, 21–34, MR1989450 (2004i:05152).

159. G. I. Bell [2007], A fresh look at peg solitaire, Math. Mag. 80(1), 16–28, MR2286485.

160. G. I. Bell [2007], Diagonal peg solitaire, Integers, Electr. J. of Combinat. Number Theory 7, #G01, 20 pp., MR2282183 (2007j:05018).

http://www.integers-ejcnt.org/vol7.html

161. G. I. Bell [2008], Solving triangular peg solitaire, J. Integer Seq. 11, Article 08.4.8, 22, 2457078 (2009h:91050).

162. G. I. Bell [2009], The shortest game of Chinese checkers and related problems, Integers 9, G01, 22, MR2475631 (2010a:91035).

http://dx.doi.org/10.1515/INTEG.2009.003

163. G. I. Bell, D. S. Hirschberg and P. Guerrero-García [2007], The minimum size required of a solitaire army, Integers, Electr. J. of Combinat. Number Theory 7, #G07, 22 pp., MR2342185.

http://www.integers-ejcnt.org/vol7.html

164. J. Bell and B. Stevens [2007], Constructing orthogonal pandiagonal Latin squares and panmagic squares from modular n-queens solutions, J. Combin. Des. 15, 221–234, 2311190 (2008c:05022).

http://dx.doi.org/10.1002/jcd.20143

165. J. Bell and B. Stevens [2008], Results for the n-queens problem on the Möbius board, Australas. J. Combin. 42, 21–34, 2445795 (2009h:05049).

166. J. Bell and B. Stevens [2009], A survey of known results and research areas for n-queens, Discrete Math. 309, 1–31, 2474997 (2010a:05002).

http://dx.doi.org/10.1016/j.disc.2007.12.043

167. R. C. Bell [1960, 1969], Board and Table Games from Many Civilisations, Vol. I & II, Oxford University Press, revised in 1979, Dover.

168. R. Bell and M. Cornelius [1988], Board Games Round the World: A Resource Book for Mathematical Investigations, Cambridge University Press, Cambridge, reprinted 1990.

169. A. J. Benjamin, M. T. Fluet and M. L. Huber [2001], Optimal Token Allocations in Solitaire Knock ’m Down, Electr. J. Combin. 8(2), #R2, 8 pp., Volume in honor of Aviezri S. Fraenkel, MR1853253 (2002g:91048).

http://www.combinatorics.org/

170. S. J. Benkoski, M. G. Monticino and J. R. Weisinger [1991], A survey of the search theory literature, Naval Res. Logistics 38, 469–494.

171. G. Bennett [1994], Double dipping: the case of the missing binomial coefficient identities, Theoret. Comput. Sci. (Math Games) 123, 351–375.

172. H.-J. Bentz [1987], Proof of the Bulgarian Solitaire conjectures, Ars Combin. 23, 151–170, MR886950 (88k:05018).

173. A. Berarducci and B. Intrigila [1993], On the cop number of a graph, Adv. in Appl. Math. 14, 389–403, 1246413 (94g:05079).

http://dx.doi.org/10.1006/aama.1993.1019

174. E. Berkove, J. Van Sickle, B. Hummon and J. Kogut [2008], An analysis of the (colored cubes)^{3} puzzle, Discrete Math. 308(7), 1033–1045, MR2382343.

175. D. Berend and A. Sapir [2006], The cyclic multi-peg tower of Hanoi, ACM Trans. Algorithms 2, 297–317, MR2253783.

176. D. Berend and A. Sapir [2006], The diameter of Hanoi graphs, Inform. Process. Lett. 98, 79–85, MR2207581 (2006m:68187).

177. D. Berengut [1981], A random hopscotch problem or how to make Johnny read more, in: The Mathematical Gardner (D. A. Klarner, ed.), Wadsworth Internat., Belmont, CA, pp. 51–59.

178. B. Berezovskiy and A. Gnedin [1984], The best choice problem, Akad. Nauk, USSR, Moscow (in Russian) .

179. C. Berge [1956], La fonction de Grundy d’un graphe infini, C. R. Acad. Sci. Paris 242, 1404–1407, MR0089115 (19,621d).

180. C. Berge [1957], Théorie générale des jeux à n personnes, Mémor. Sci. Math., no. 138, Gauthier-Villars, Paris, MR0099259 (20 #5700).

181. C. Berge [1976], Sur les jeux positionnels, Cahiers du Centre Études Rech. Opér. 18, 91–107.

182. C. Berge [1977], Vers une théorie générale des jeux positionnels, in: Mathematical Economics and Game Theory, Essays in Honor of Oskar Morgenstern, Lecture Notes in Economics (R. Henn and O. Moeschlin, eds.), Vol. 141, Springer Verlag, Berlin, pp. 13–24.

183. C. Berge [1981], Some remarks about a Hex problem, in: The Mathematical Gardner (D. A. Klarner, ed.), Wadsworth Internat., Belmont, CA, pp. 25–27.

184. C. Berge [1982], Les jeux combinatoires, Cahiers Centre Études Rech. Opér. 24, 89–105, MR687875 (84d:90112).

185. C. Berge [1985], Graphs, North-Holland, Amsterdam, Chap. 14.

186. C. Berge [1989], Hypergraphs, Elsevier (French: Gauthier Villars 1988), Chap. 4.

187. C. Berge [1992], Les jeux sur un graphe, Cahiers Centre Études Rech. Opér. 34, 95–101, MR1226531 (94h:05089).

188. C. Berge [1996], Combinatorial games on a graph, Discrete Math. 151(1-3), 59–65, Graph theory and combinatorics (Manila, 1991), 1391251 (97c:90159).

http://dx.doi.org/10.1016/0012-365X(94)00081-S

189. C. Berge and P. Duchet [1988], Perfect graphs and kernels, Bull. Inst. Math. Acad. Sinica 16, 263–274.

190. C. Berge and P. Duchet [1990], Recent problems and results about kernels in directed graphs, Discrete Math. 86, 27–31, appeared first under the same title in Applications of Discrete Mathematics (Clemson, SC, 1986), 200–204, SIAM, Philadelphia, PA, 1988.

191. C. Berge and M. Las Vergnas [1976], Un nouveau jeu positionnel, le “Match-It”, ou une construction dialectique des couplages parfaits, Cahiers du Centre Études Rech. Opér. 18, 83–89.

192. C. Berge and M. P. Schützenberger [1956], Jeux de Nim et solutions, Acad. Sci. Paris 242, 1672–1674, (French).

193. E. R. Berlekamp [1972], Some recent results on the combinatorial game called Welter’s Nim, Proc. 6th Ann. Princeton Conf. Information Science and Systems, pp. 203–204.

194. E. R. Berlekamp [1974], The Hackenbush number system for compression of numerical data, Inform. and Control 26, 134–140.

195. E. R. Berlekamp [1988], Blockbusting and domineering, J. Combin. Theory (Ser. A) 49, 67–116, an earlier version, entitled Introduction to blockbusting and domineering, appeared in: The Lighter Side of Mathematics, Proc. E. Strens Memorial Conf. on Recr. Math. and its History, Calgary, 1986, Spectrum Series (R. K. Guy and R. E. Woodrow, eds.), Math. Assoc. of America, Washington, DC, 1994, pp. 137–148.

196. E. Berlekamp [1990], Two-person, perfect-information games, in: The Legacy of John von Neumann (Hempstead NY, 1988), Proc. Sympos. Pure

Math., Vol. 50, Amer. Math. Soc., Providence, RI, pp. 275–287.

197. E. R. Berlekamp [1991], Introductory overview of mathematical Go endgames, in: Combinatorial Games, Proc. Symp. Appl. Math. (R. K. Guy, ed.), Vol. 43, Amer. Math. Soc., Providence, RI, pp. 73–100.

198. E. Berlekamp [1996], The economist’s view of combinatorial games, in: Games of no chance (Berkeley, CA, 1994), Vol. 29 of Math. Sci. Res. Inst. Publ., Cambridge Univ. Press, Cambridge, pp. 365–405, 1427978 (97j:90098).

199. E. R. Berlekamp [2000], Sums of N × 2 Amazons, in: Institute of Mathematical Statistics Lecture Notes–Monograph Series (F.T. Bruss and L.M. Le Cam, eds.), Vol. 35, Beechwood, Ohio: Institute of Mathematical Statistics, pp. 1–34, Papers in honor of Thomas S. Ferguson, MR1833848 (2002e:91033).

200. E. R. Berlekamp [2000], The Dots-and-Boxes Game: Sophisticated Child’s Play, A K Peters, Natick, MA, MR1780088 (2001i:00005).

201. E. R. Berlekamp [2002], Four games for Gardner, in: Puzzler’s Tribute: a Feast for the Mind, pp. 383–386, honoring Martin Gardner (D. Wolfe and T. Rodgers, eds.), A K Peters, Natick, MA.

202. E. R. Berlekamp [2002], Idempotents among partisan games, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 3–23.

203. E. R. Berlekamp [2002], The 4G4G4G4G4 problems and solutions, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 231–241.

204. E. R. Berlekamp [2009], Yellow-brown Hackenbush, in: Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 413–418.

205. E. R. Berlekamp, J. H. Conway and R. K. Guy [2001-2004], Winning Ways for your Mathematical Plays, Vol. 1-4, A K Peters, Wellesley, MA, 2nd edition: vol. 1 (2001), vols. 2, 3 (2003), vol. 4 (2004); translation of 1st edition (1982) into German: Gewinnen, Strategien für Mathematische Spiele by G. Seiffert, Foreword by K. Jacobs, M. Reményi and Seiffert, Friedr. Vieweg & Sohn, Braunschweig (four volumes), 1985.

206. E. R. Berlekamp and Y. Kim [1996], Where is the “Thousand-Dollar Ko?”, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 203–226.

207. E. Berlekamp and T. Rodgers, eds. [1999], The Mathemagician and Pied Puzzler, A K Peters, Natick, MA, A collection in tribute to Martin Gardner. Papers from the Gathering for Gardner Meeting (G4G1) held in Atlanta, GA, January 1993.

208. E. Berlekamp and K. Scott [2002], Forcing your opponent to stay in control of a loony dots-and-boxes endgame, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 317–330, MR1973020.

209. E. Berlekamp and D. Wolfe [1994], Mathematical Go, A K Peters Ltd., Wellesley, MA, Chilling gets the last point, With a foreword by James Davies, 1274921 (95i:90131).

210. P. Berloquin [1976], 100 Jeux de Table, Flammarion, Paris.

211. P. Berloquin [1995], 100 Games of Logic, Barnes & Noble.

212. P. Berloquin and D. Dugas (Illustrator) [1999], 100 Perceptual Puzzles, Barnes & Noble.

213. A. M. Bersani [2010], Reformed permutations in Mousetrap and its generalizations, Integers 10, G01, 575–622, 2797780 (2012d:05021).

http://dx.doi.org/10.1515/INTEG.2010.101

214. S. Bhattacharya, G. Paul and S. Sanyal [2010], A cops and robber game in multidimensional grids, Discrete Appl. Math. 158(16), 1745–1751, 2679773 (2012b:05178).

http://dx.doi.org/10.1016/j.dam.2010.06.014

215. T. C. Biedl, E. D. Demaine, M. L. Demaine, R. Fleischer, L. Jacobsen and I. Munro [2002], The complexity of Clickomania, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 389–404, MR1973107 (2004b:91041).

216. N. L. Biggs [1999], Chip-firing and the critical group of a graph, J. Algebr. Comb. 9, 25–45.

217. K. Binmore [1992], Fun and Games: a Text on Game Theory, D.C. Heath, Lexington.

218. J. Bitar and E. Goles [1992], Parallel chip firing games on graphs, Theoret. Comput. Sci. 92, 291–300.

219. J. Björklund and C. Holmgren [2012], Counterexamples to a monotonicity conjecture for the threshold pebbling number, Discrete Math. 312, 2401– 2405.

220. A. Björner and L. Lovász [1992], Chip-firing games on directed graphs, J. Algebraic Combin. 1, 305–328.

221. A. Björner, L. Lovász and P. W. Shor [1991], Chip-firing games on graphs, European J. Combin. 12(4), 283–291, 1120415 (92g:90193).

222. Y. Björnsson, R. Hayward, M. Johanson and J. van Rijswijck [2007], Dead cell analysis in Hex and the Shannon game, in: Graph theory in Paris, Trends Math., Birkhäuser, Basel, pp. 45–59, MR2279166 (2007j:91023).

223. N. M. Blachman and D. M. Kilgour [2001], Elusive optimality in the box problem, Math. Mag. 74(3), 171–181, MR2104911.

224. D. Blackwell and M. A. Girshick [1954], Theory of Games and Statistical Decisions, Wiley, New York, NY.

225. L. Blanc, E. Duchêne and S. Gravier [2006], A deletion game on graphs: le pic arête, Integers, Electr. J. of Combinat. Number Theory 6, #G02, 10 pp., Comb. Games Sect., MR2215359.

http://www.integers-ejcnt.org/vol5.html

226. S. Blanco and A. S. Fraenkel [2011], Tromping games: tiling with trominoes, Integers, Electr. J of Combinat. Number Theory 11A, #6, 29 pp., Proc. INTEGERS Conference in honor of the birthdays of Melvyn Nathanson and Carl Pomeranc, Carrollton, GA, Oct. 14-17, 2009.

227. U. Blass and A. S. Fraenkel [1990], The Sprague-Grundy function for Wythoff’s game, Theoret. Comput. Sci. 75(3), 311–333, MR1080539 (92a:90101).

228. U. Blass, A. S. Fraenkel and R. Guelman [1998], How far can nim in diguise be stretched?, J. Combin. Theory Ser. A 84(2), 145–156, 1652900 (2000d:91029).

http://dx.doi.org/10.1006/jcta.1998.2882

229. M. Blidia [1986], A parity digraph has a kernel, Combinatorica 6, 23–27.

230. M. Blidia, P. Duchet, H. Jacob, F. Maffray and H. Meyniel [1999], Some operations preserving the existence of kernels, Discrete Math. 205, 211– 216.

231. M. Blidia, P. Duchet and F. Maffray [1993], On kernels in perfect graphs, Combinatorica 13, 231–233.

232. V. D. Blondel, J. M. Hendrickx and R. M. Jungers [2008], Solitaire Clobber as an optimization problem on words, Integers 8, G04, 12, MR2425633 (2009d:91038).

233. G. Bloom, M. Lampis, F. A. Muntaner-Batle and M. Rius-Font [2011], Queen labelings, AKCE Int. J. Graphs Comb. 8(1), 13–22, 2839172 (2012f:05252).

234. J.-P. Bode and H. Harborth [1998], Achievement games on Platonic solids, Bull. Inst. Combin. Appl. 23, 23–32, MR1621748 (99d:05020).

235. J.-P. Bode and H. Harborth [2000], Hexagonal polyomino achievement, Discrete Math. 212, 5–18, MR1748669 (2000k:05082).

236. J.-P. Bode and H. Harborth [2000], Independent chess pieces on Euclidean boards, J. Combin. Math. Combin. Comput. 33, 209–223, MR1772763 (2001c:05105).

237. J.-P. Bode and H. Harborth [2000], Triangular mosaic polyomino achievement, Congr. Numer. 144, 143–152, Proc. 31st Southeastern Internat. Conf. on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 2000), MR1817929 (2001m:05082).

238. J.-P. Bode and H. Harborth [2001], Triangle polyomino set achievement, Congr. Numer. 148, 97–101, Proc.32nd Southeastern Internat. Conf. on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 2002), MR1887377 (2002k:05057).

239. J.-P. Bode and H. Harborth [2002], Triangle and hexagon gameboard Ramsey numbers, Congr. Numer. 158, 93–98, Proc.33rd Southeastern Internat. Conf. on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 2002), MR1985149 (2004d:05129).

240. J.-P. Bode and H. Harborth [2003], Independence for knights on hexagon and triangle boards, Discrete Math. 272, 27–35, MR2019197 (2004i:05115).

241. J.-P. Bode, H. Harborth and M. Harborth [2003], King independence on triangle boards, Discrete Math. 266, 101–107, Presented at 18th British Combinatorial Conference (Brighton, 2001), MR1991709 (2004f:05129).

242. J.-P. Bode, H. Harborth and M. Harborth [2004], King graph Ramsey numbers, J. Combin. Math. Combin. Comput. 50, 47–55, MR2075855.

243. J.-P. Bode, H. Harborth and H. Weiss [1999], Independent knights on hexagon boards, Congr. Numer. 141, 31–35, Proc. 30th Southeastern Internat. Conf. on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1999), MR1745222 (2000k:05201).

244. J.-P. Bode and A. M. Hinz [1999], Results and open problems on the Tower of Hanoi, Congr. Numer. 139, 113–122, Proc.30th Southeastern Internat. Conf. on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1999).

245. H. L. Bodlaender [1991], On the complexity of some coloring games, Internat. J. Found. Comput. Sci. 2, 133–147, MR1143920 (92j:68042).

246. H. L. Bodlaender [1993], Complexity of path forming games, Theoret. Comput. Sci. (Math Games) 110, 215–245.

247. H. L. Bodlaender [1993], Kayles on special classes of graphs—an application of Sprague-Grundy theory, in: Graph-Theoretic Concepts in Computer Science (Wiesbaden-Naurod, 1992), Lecture Notes in Comput. Sci., Vol. 657, Springer, Berlin, pp. 90–102, MR1244129 (94i:90189).

248. H. L. Bodlaender and D. Kratsch [1992], The complexity of coloring games on perfect graphs, Theoret. Comput. Sci. (Math Games) 106, 309–326.

249. H. L. Bodlaender and D. Kratsch [2002], Kayles and nimbers, J. Algorithms 43, 106–119, MR1900711 (2003d:05201).

250. H. L. Bodlaender, S. Thomassé and A. Yeo [2011], Kernel bounds for disjoint cycles and disjoint paths, Theoret. Comput. Sci. 412(35), 4570– 4578, 2850415.

http://dx.doi.org/10.1016/j.tcs.2011.04.039

251. T. Bohman, R. Holzman and D. Kleitman [2001], Six Lonely Runners, Electr. J. Combin. 8(2), #R3, 49 pp., Volume in honor of Aviezri S. Fraenkel, MR1853254 (2002g:11095).

http://www.combinatorics.org/

252. T. Bohman, O. Pikhurko, A. Frieze and D. Sleator, Hat problems, The Puzzle Toad.

http://www.cs.cmu.edu/puzzle/solution15.pdf

253. K. D. Boklan [1984], The n-number game, Fibonacci Quart. 22, 152–155.

254. B. Bollobás and I. Leader [2006], The angel and the devil in three dimensions, J. Combin. Theory Ser. A 113(1), 176–184, 2192775 (2006h:05030).

http://dx.doi.org/10.1016/j.jcta.2005.03.009

255. B. Bollobás and T. Szabó [1998], The oriented cycle game, Discrete Math. 186, 55–67.

256. A. Bonato, E. Chiniforooshan and P. Prałat [2010], Cops and Robbers from a distance, Theoret. Comput. Sci. 411(43), 3834–3844, 2779754 (2012d:05251).

http://dx.doi.org/10.1016/j.tcs.2010.07.003

257. A. Bonato, P. Golovach, G. Hahn and J. Kratochvíl [2009], The capture time of a graph, Discrete Math. 309(18), 5588–5595, 2567962 (2010j:05273).

http://dx.doi.org/10.1016/j.disc.2008.04.004

258. A. Bonato, G. Hahn and C. Tardif [2010], Large classes of infinite k-cop-win graphs, J. Graph Theory 65(4), 334–342, 2744858 (2011k:05157).

http://dx.doi.org/10.1002/jgt.20484

259. A. Bonato, G. Hahn and C. Wang [2007], The cop density of a graph, Contrib. Discrete Math. 2(2), 133–144 (electronic), 2358266 (2009b:05224).

260. A. Bonato, G. Kemkes and P. Prałat [2012], Almost all cop-win graphs contain a universal vertex, Discrete Math. 312, 1652–1657.

261. A. Bonato and R. J. Nowakowski [2011], The game of cops and robbers on graphs, Vol. 61 of Student Mathematical Library, American Mathematical Society, Providence, RI, 2830217.

262. A. Bonato, P. Prałat and C. Wang [2007], Pursuit-evasion in models of complex networks, Internet Math. 4(4), 419–436, 2522951 (2011d:68008).

http://projecteuclid.org/getRecord?id=euclid.im/1243430813

263. D. L. Book [1998, Sept. 9-th], What the Hex, The Washington Post p. H02.

264. E. Borel [1921], La théorie du jeu et les équations integrales à noyau symmetrique gauche, C. R. Acad. Sci. Paris 173, 1304–1308.

265. E. Boros and V. Gurvich [1996], Perfect graphs are kernel solvable, Discrete Math. 159, 35–55.

266. E. Boros and V. Gurvich [1998], A corrected version of the Duchet kernel conjecture, Discrete Math. 179, 231–233.

267. E. Boros and V. Gurvich [2006], Perfect graphs, kernels, and cores of cooperative games, Discrete Math. 306(19-20), 2336–2354, MR2261906 (2007g:05069).

268. M. Borowiecki, S. Jendrol’, D. Král and J. Miškuf [2006], List coloring of Cartesian products of graphs, Discrete Math. 306, 1955–1958, MR2251575 (2007b:05067).

269. M. Borowiecki and E. Sidorowicz [2007], Generalised game colouring of graphs, Discrete Math. 307(11-12), 1225–1231, MR2311092.

270. M. Borowiecki, E. Sidorowicz and Z. Tuza [2007], Game list colouring of graphs, Electron. J. Combin. 14(1), #R26, 11 pp., MR2302533.

271. E. Boudreau, B. Hartnell, K. Schmeisser and J. Whiteley [2004], A game based on vertex-magic total labelings, Australas. J. Combin. 29, 67–73,

MR2037334 (2004k:91059).

272. C. L. Bouton [1902], Nim, a game with a complete mathematical theory, Ann. of Math. 3(2), 35–39.

273. B. H. Bowditch [2007], The angel game in the plane, Combin. Probab. Comput. 16, 345–362, MR2312431 (2008a:91036).

274. J. Boyce [1981], A Kriegspiel endgame, in: The Mathematical Gardner (D. A. Klarner, ed.), Wadsworth Internat., Belmont, CA, pp. 28–36.

275. S. J. Brams and D. M. Kilgour [1995], The box problem: to switch or not to switch, Math. Mag. 68(1), 27–34.

276. G. Brandreth [1981], The Bumper Book of Indoor Games, Victorama, Chancellor Press.

277. B. Brešar, S. Klavžar and D. F. Rall [2010], Domination game and an imagination strategy, SIAM J. Discrete Math. 24(3), 979–991, 2680228 (2011g:05202).

http://dx.doi.org/10.1137/100786800

278. B. Brešar, S. Klavžar and D. F. Rall [2013], Domination game played on trees and spanning subgraphs, Discrete Math. 313(8), 915–923, 3021500.

http://dx.doi.org/10.1016/j.disc.2013.01.014

279. D. M. Breuker, J. W. H. M. Uiterwijk and H. J. van den Herik [2000], Solving 8 × 8 Domineering, Theoret. Comput. Sci. (Math Games) 230, 195–206, MR1725637 (2001i:68148).

280. D. M. Broline and D. E. Loeb [1995], The combinatorics of Mancala-type games: Ayo, Tchoukaillon, and 1/π, UMAP J. 16(1), 21–36.

281. A. Brousseau [1976], Tower of Hanoi with more pegs, J. Recr. Math. 8, 169–176.

282. A. E. Brouwer, G. Horváth, I. Molnár-Sáska and C. Szabó [2005], On three-rowed chomp, Integers, Electr. J. of Combinat. Number Theory 5, #G07, 11 pp., Comb. Games Sect., MR2192255 (2006g:11051).

http://www.integers-ejcnt.org/vol5.html

283. C. Browne [2000], HEX Strategy: Making the Right Connections, A K Peters, Natick, MA.

284. C. Browne [2005], Connection Games: Variations on a Theme, A K Peters, Natick, MA.

285. C. Browne [2006], Fractal board games., Computers & Graphics 30(1), 126–133.

286. R. A. Brualdi and V. S. Pless [1993], Greedy codes, J. Combin. Theory (Ser. A) 64, 10–30.

287. A. A. Bruen and R. Dixon [1975], The n-queen problem, Discrete Math. 12, 393–395.

288. J. Bruno and L. Weinberg [1970], A constructive graph-theoretic solution of the Shannon switching game, IEEE Trans. Circuit Theory CT-17, 74–81.

289. G. P. Bucan and L. P. Varvak [1966], On the question of games on a graph, in: Algebra and Math. Logic: Studies in Algebra (Russian), Izdat.

Kiev. Univ., Kiev, pp. 122–138, MR0207584 (34 #7399).

290. J. P. Buhler [2002], Hat tricks, Math. Intelligencer 24, 44–49, MR1930867 (2003g:00006).

http://dx.doi.org/10.1007/BF03025323

291. B. Bukh [2006], Maximum pebbling number of graphs of diameter three, J. Graph Theory 52, 353–357, MR2242834 (2007i:05090).

292. P. Buneman and L. Levy [1980], The towers of Hanoi problem, Inform. Process. Lett. 10, 243–244.

293. A. P. Burger, E. J. Cockayne and C. M. Mynhardt [1997], Domination and irredundance in the queen’s graph, Discrete Math. 163, 47–66, MR1428557 (97m:05130).

294. A. P. Burger and C. M. Mynhardt [1999], Queens on hexagonal boards, J. Combin. Math. Combin. Comput. 31, 97–111, paper in honour of Stephen T. Hedetniemi, MR1726950 (2000h:05158).

295. A. P. Burger and C. M. Mynhardt [2000], Properties of dominating sets of the queens graph Q_{4k+3}, Util. Math. 57, 237–253, MR1760187 (2000m:05166).

296. A. P. Burger and C. M. Mynhardt [2000], Small irredundance numbers for queens graphs, J. Combin. Math. Combin. Comput. 33, 33–43, paper in honour of Ernest J. Cockayne, MR1772752 (2001c:05106).

297. A. P. Burger and C. M. Mynhardt [2000], Symmetry and domination in queens graphs, Bull. Inst. Combin. Appl. 29, 11–24.

298. A. P. Burger and C. M. Mynhardt [2002], An upper bound for the minimum number of queens covering the n × n chessboard, Discrete Appl. Math. 121, 51–60.

299. A. P. Burger and C. M. Mynhardt [2003], An improved upper bound for queens domination numbers, Discrete Math. 266, 119–131.

300. A. P. Burger, C. M. Mynhardt and E. J. Cockayne [1994], Domination numbers for the queen’s graph, Bull. Inst. Combin. Appl. 10, 73–82.

301. A. P. Burger, C. M. Mynhardt and E. J. Cockayne [2001], Queens graphs for chessboards on the torus, Australas. J. Combin. 24, 231–246.

302. K. W. Burke and S.-H. Teng [2008], Atropos: a PSPACE-complete Sperner triangle game, Internet Math. 5(4), 477–492 (2009), 2604973 (2011d:05240).

http://projecteuclid.org/getRecord?id=euclid.im/1265033176

303. M. Buro [2001], Simple Amazon endgames and their connection to Hamilton circuits in cubic subgrid graphs, Proc. 2nd Intern. Conference on Computers and Games CG’2000 (T. Marsland and I. Frank, eds.), Vol. 2063, Hamamatsu, Japan, Oct. 2000, Lecture Notes in Computer Science, Springer, pp. 251–261, MR1909614.

304. D. W. Bushaw [1967], On the name and history of Nim, Washington Math. 11, Oct. 1966. Reprinted in: NY State Math. Teachers J., 17, pp. 52–55.

305. S. Butler, M. T. Hajiaghayi, R. D. Kleinberg and T. Leighton [2008], Hat guessing games, SIAM J. Discrete Math. 22(2), 592–605, Reprinted in SIAM Rev. 51 (2009), 399–413, MR2399367 (2009f:91016).

http://dx.doi.org/10.1137/060652774

306. P. J. Byrne and R. Hesse [1996], A Markov chain analysis of jai alai, Math. Mag. 69, 279–283.

307. S. Byrnes [2003], Poset game periodicity, Integers, Electr. J. of Combinat. Number Theory 3, #G3, 16 pp., Comb. Games Sect., MR2036487 (2005c:91031).

http://www.integers-ejcnt.org/vol3.html

308. J.-Y. Cai, A. Condon and R. J. Lipton [1992], On games of incomplete information, Theoret. Comput. Sci. 103, 25–38.

309. L. Cai and X. Zhu [2001], Game chromatic index of k-degenerate graphs, J. Graph Theory 36, 144–155, MR1814531 (2002b:05058).

310. G. Cairns [2002], Pillow chess, Math. Mag. 75, 173–186, MR2075210 (2005b:91011).

311. G. Cairns and N. B. Ho [2010], Min, a combinatorial game having a connection with prime numbers, Integers 10, G03, 765–770, 2797778.

http://dx.doi.org/10.1515/INTEG.2010.103

312. G. Cairns and N. B. Ho [2010], Ultimately bipartite subtraction games, Australas. J. Combin. 48, 213–220, 2732114 (2011m:05199).

313. G. Cairns and N. B. Ho [2011], Some remarks on End-Nim, Int. J. Comb. pp. Art. ID 824742, 9, 2861127.

314. G. Cairns, N. B. Ho and T. Lengyel [2011], The Sprague-Grundy function of the real game Euclid, Discrete Math. 311(6), 457–462, 2799898.

http://dx.doi.org/10.1016/j.disc.2010.12.011

315. D. Calistrate [1996], The reduced canonical form of a game, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 409–416, MR1427979 (97m:90122).

316. D. Calistrate, M. Paulhus and D. Wolfe [2002], On the lattice structure of finite games, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 25–30, MR1973001.

317. N. J. Calkin, K. James, J. E. Janoski, S. Leggett, B. Richards, N. Sitaraman and S. M. Thomas [2010], Computing strategies for graphical Nim, Proceedings of the Forty-First Southeastern International Conference on Combinatorics, Graph Theory and Computing, Vol. 202, pp. 171–185, 2762470 (2011j:05222).

318. N. J. Calkin, K. James, S. Purvis, S. Race, K. Schneider and M. Yancey [2006], Counting kings: explicit formulas, recurrence relations, and generating functions! Oh my!, Proceedings of the Thirty-Seventh Southeastern International Conference on Combinatorics, Graph Theory and Computing, Vol. 182, pp. 41–51, 2311287.

319. N. J. Calkin, K. James, S. Purvis, S. Race, K. Schneider and M. Yancey [2006], Counting kings: as easy as λ_{1}, λ_{2}, λ_{3} …, Proceedings of the Thirty-Seventh Southeastern International Conference on Combinatorics, Graph Theory and Computing, Vol. 183, pp. 83–95, 2311471.

320. G. Campbell [2004], On optimal play in the game of Hex, Integers, Electr. J. of Combinat. Number Theory 4, #G2, 23 pp., Comb. Games Sect., MR2056016 (2005c:91032).

http://www.integers-ejcnt.org/vol4.html

321. C. Cannings and J. Haigh [1992], Montreal solitaire, J. Combin. Theory (Ser. A) 60, 50–66.

322. J. Carlson and D. Stolarski [2004], The correct solution to Berlekamp’s switching game, Discrete Math. 287, 145–150, MR2094708 (2005d:05005).

323. J. Carraher, I. Choi, M. Delcourt, L. H. Erickson and D. B. West [2012], Locating a robber on a graph via distance queries, Theoret. Comput. Sci. 463, 54–61, 2992497.

http://dx.doi.org/10.1016/j.tcs.2012.06.035

324. A. Carvalho and C. Pereira dos Santos [2010], Chess and mathematics, in: Recreational Mathematics Colloquium I , Assoc. Ludus, Lisbon, pp. 3–26, 2807390.

325. A. Carvalho, C. Santos, C. Dias, F. Coelho, J. Neto, and S. Vinagre [2012], A recursive process related to a partizan version of Wythoff, Integers, Electr. J. of Combinat. Number Theory 12, #G3, 15 pp., Comb. Games Sect.

http://www.integers-ejcnt.org/vol12.html

326. J. Chalopin, V. Chepoi, N. Nisse and Y. Vaxès [2011], Cop and robber games when the robber can hide and ride, SIAM J. Discrete Math. 25(1), 333–359, 2801232.

http://dx.doi.org/10.1137/100784035

327. M. Chan and A. P. Godbole [2008], Improved pebbling bounds, Discrete Math. 308, 2301–2306, MR2404560.

328. A. Chan and A. Tsai [2002], 1×n Konane: a summary of results, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 331–339, MR1973021.

329. T.-H. Chan [1989], A statistical analysis of the towers of Hanoi problem, Intern. J. Computer Math. 28, 57–65.

330. A. K. Chandra, D. C. Kozen and L. J. Stockmeyer [1981], Alternation, J. Assoc. Comput. Mach. 28, 114–133.

331. A. K. Chandra and L. J. Stockmeyer [1976], Alternation, Proc. 17th Ann. Symp. Foundations of Computer Science (Houston, TX, Oct. 1976), IEEE Computer Soc., Long Beach, CA, pp. 98–108.

332. H. Chang and X. Zhu [2006], The d-relaxed game chromatic index of k-degenerated graphs, Australas. J. Combin. 36, 73–82, MR2262608.

333. H. Chang and X. Zhu [2009], Colouring games on outerplanar graphs and trees, Discrete Math. 309(10), 3185–3196, 2526737 (2011a:05097).

http://dx.doi.org/10.1016/j.disc.2008.09.015

334. G. Chartrand, F. Harary, M. Schultz and D. W. VanderJagt [1995], Achievement and avoidance of a strong orientation of a graph, Congr. Numer. 108, 193–203.

335. S. M. Chase [1972], An implemented graph algorithm for winning Shannon switching games, Commun. Assoc. Comput. Mach. 15, 253–256.

336. M. Chastand, F. Laviolette and N. Polat [2000], On constructible graphs, infinite bridged graphs and weakly cop-win graphs, Discrete Math. 224, 61–78, MR1781285 (2002g:05152).

337. V. Chatelain and J. L. Ramírez Alfonsín [2012], The switching game on unions of oriented matroids, European J. Combin. 33(2), 215–219, 2854642.

http://dx.doi.org/10.1016/j.ejc.2011.08.006

338. G. Chen, R. H. Schelp and W. E. Shreve [1997], A new game chromatic number, European J. Combin. 18(1), 1–9, 1427601 (97k:05071).

http://dx.doi.org/10.1006/eujc.1994.0071

339. L.-J. Chen, J.-J. Lin, M.-Z. Shieh and S.-C. Tsai [2011], More on the Magnus-Derek game, Theoret. Comput. Sci. 412(4-5), 339–344, 2778466 (2012c:91059).

http://dx.doi.org/10.1016/j.tcs.2010.09.031

340. R. W. Chen, A. Zame and B. Rosenberg [2009], On the first occurrence of strings, Electron. J. Combin. 16(1), Research Paper 29, 16, MR2482097 (2010h:91058).

http://www.combinatorics.org/Volume_16/Abstracts/v16i1r29.
html

341. X. Chen, X. Deng and S.-H. Teng [2009], Settling the complexity of computing two-player Nash equilibria, J. ACM 56(3), Art. 14, 57, 2536129 (2010i:68040).

http://dx.doi.org/10.1145/1516512.1516516

342. V. Chepoi [1997], Bridged graphs are cop-win graphs: an algorithmic proof, J. Combin. Theory (Ser. B) 69, 97–100.

343. S.-H. Chiang, I.-C. Wu and P.-H. Lin [2011], Drawn k-in-a-row games, Theoret. Comput. Sci. 412(35), 4558–4569, 2850414.

http://dx.doi.org/10.1016/j.tcs.2011.04.033

344. B. S. Chlebus [1986], Domino-tiling games, J. Comput. System Sci. 32, 374–392.

345. C.-Y. Chou, W. Wang and X. Zhu [2003], Relaxed game chromatic number of graphs, Discrete Math. 262, 89–98, MR1951379 (2003m:05062).

346. T. Y. Chow, H. Eriksson and C. K. Fan [2004/06], Chess tableaux, Electron. J. Combin. 11(2), Article 3, 18 pp. (electronic), 2195434 (2006i:05172).

http://www.combinatorics.org/Volume_11/Abstracts/v11i2a3.
html

347. J. D. Christensen and M. Tilford [1997], Unsolved Problems: David Gale’s subset take-away game, Amer. Math. Monthly 104, 762–766, Unsolved Problems Section.

348. F. R. K. Chung [1989], Pebbling in hypercubes, SIAM J. Disc. Math. 2, 467–472.

349. F. R. K. Chung, J. E. Cohen and R. L. Graham [1988], Pursuit-evasion games on graphs, J. Graph Theory 12, 159–167.

350. F. Chung and R. B. Ellis [2002], A chip-firing game and Dirichlet eigenvalues, Discrete Math. 257, 341–355, MR1935732 (2003i:05087).

351. F. Chung, R. Graham, J. Morrison and A. Odlyzko [1995], Pebbling a chessboard, Amer. Math. Monthly 102, 113–123.

352. V. Chvátal [1973], On the computational complexity of finding a kernel, Report No. CRM-300, Centre de Recherches Mathématiques, Université de Montréal.

353. V. Chvátal [1981], Cheap, middling or dear, in: The Mathematical Gardner (D. A. Klarner, ed.), Wadsworth Internat., Belmont, CA, pp. 44–50.

354. V. Chvátal [1983], Mastermind, Combinatorica 3, 325–329.

355. V. Chvátal and P. Erdős [1978], Biased positional games, Ann. Discrete Math. 2, 221–229, Algorithmic Aspects of Combinatorics, (B. Alspach, P. Hell and D. J. Miller, eds.), Qualicum Beach, BC, Canada, 1976, North-Holland.

356. P. Ciancarini and G. P. Favini [2010], Monte Carlo tree search in Kriegspiel, Artificial Intelligence 174(11), 670–684, 2723431 (2011j:91060).

http://dx.doi.org/10.1016/j.artint.2010.04.017

357. P. Ciancarini and G. P. Favini [2010], Playing the perfect Kriegspiel endgame, Theoret. Comput. Sci. 411(40-42), 3563–3577, 2724085 (2011h:91055).

http://dx.doi.org/10.1016/j.tcs.2010.05.019

358. J. Cibulka, J. Kynčl, V. Mészáros, R. Stolař and P. Valtr [2009], Solution of Peter Winkler’s pizza problem, in: Combinatorial algorithms, Vol. 5874 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 356–367, 2577951.

http://dx.doi.org/10.1007/978-3-642-10217-2_35

359. J. Cibulka, J. Kynčl, V. Mészáros, R. Stolař and P. Valtr [2010], Graph sharing games: complexity and connectivity, in: Theory and applications of models of computation, Vol. 6108 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 340–349, 2755359 (2012d:91049).

http://dx.doi.org/10.1007/978-3-642-13562-0_31

360. F. Cicalese and C. Deppe [2003], Quasi-perfect minimally adaptive q-ary search with unreliable tests, in: Algorithms and Computation, Vol. 2906 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 527–536, MR2088232 (2005d:68101).

361. F. Cicalese, C. Deppe and D. Mundici [2004], Q-ary Ulam-Rényi game with weighted constrained lies, in: Computing and Combinatorics, Vol.

3106 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 82–91, MR2162023 (2006c:68037).

362. F. Cicalese and D. Mundici [1999], Optimal binary search with two unreliable tests and minimum adaptiveness, in: Algorithms—ESA ’99 (Prague), Vol. 1643 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 257–266, MR1729129 (2000i:68035).

363. F. Cicalese, D. Mundici and U. Vaccaro [2000], Least adaptive optimal search with unreliable tests, in: Algorithm Theory—SWAT 2000 (Bergen), Vol. 1851 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 549–562, MR1793099 (2001k:91005).

364. F. Cicalese, D. Mundici and U. Vaccaro [2002], Least adaptive optimal search with unreliable tests, Theoret. Comput. Sci. (Math Games) 270, 877–893, MR1871101 (2003g:94052).

365. F. Cicalese and U. Vaccaro [2000], An improved heuristic for the “Ulam-Rényi game”, Inform. Process. Lett. 73, 119–124, MR1741817 (2000m:91026).

366. F. Cicalese and U. Vaccaro [2000], Optimal strategies against a liar, Theoret. Comput. Sci. 230, 167–193, MR1725636 (2001g:91040).

367. F. Cicalese and U. Vaccaro [2003], Binary search with delayed and missing answers, Inform. Process. Lett. 85, 239–247, MR1952901 (2003m:68031).

368. A. Cincotti [2005], Three-player partizan games, Theoret. Comput. Sci. 332(1-3), 367–389, MR2122510 (2005j:91018).

http://dx.doi.org/10.1016/j.tcs.2004.12.001

369. A. Cincotti [2008], The game of Cutblock, Integers 8, G06, 12, MR2425635 (2009g:91039).

370. A. Cincotti [2009], Further results on three-player domineering, Int. J. Comput. Math. Sci. 3(6), 286–288, 2735641 (2011j:91061).

371. A. Cincotti [2009], On the complexity of N-player Hackenbush, Integers 9, G03, 621–627, 2592546 (2011b:91078).

http://dx.doi.org/10.1515/INTEG.2009.049

372. A. Cincotti [2010], n-player partizan games, Theoret. Comput. Sci. 411(34-36), 3224–3234, 2676865 (2011f:91035).

http://dx.doi.org/10.1016/j.tcs.2010.05.018

373. A. Cincotti [2010], The game of synchronized quadromineering, Int. J. Comput. Math. Sci. 4(4), 183–187, 2646201 (2011f:91034).

374. A. Cincotti [2011], The game of n-player Cutcake, Theoret. Comput. Sci. 412(41), 5678–5683, 2866564.

http://dx.doi.org/10.1016/j.tcs.2011.06.036

375. A. Cincotti [2011], The lattice structure of three-player games, in: Computers and games, Vol. 6515 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 230–237, 2804004.

http://dx.doi.org/10.1007/978-3-642-17928-0_21

376. A. Cincotti [2012], The lattice structure of n-player games, Theoret. Comput. Sci. 459, 113–119.

377. A. Cincotti and H. Iida [2006], Outcome uncertainty and interestedness in game-playing: a case study using synchronized Hex, New Math. Nat. Comput. 2(2), 173–181, 2250132.

http://dx.doi.org/10.1142/S1793005706000440

378. A. Cincotti, S. Komori and H. Iida [2008], The game of synchronized triomineering and synchronized tridomineering, Int. J. Comput. Math. Sci. 2(3), 143–148, 2461334 (2011a:91087).

379. C. Clark [1996], On achieving channels in a bipolar game, in: African Americans in Mathematics (Piscataway, NJ, 1996), DIMACS Ser. Discrete Math. Theoret. Comput. Sci., Vol. 34, Amer. Math. Soc., Providence, RI, pp. 23–27.

380. D. S. Clark [1986], Fibonacci numbers as expected values in a game of chance, Fibonacci Quart. 24, 263–267.

381. S. Clark, P. Johnson and M. Walsh [2011], Edge-sensitivity of the Grundy number, Proceedings of the Forty-Second Southeastern International Conference on Combinatorics, Graph Theory and Computing, Vol. 207, pp. 171–180, 2856318.

382. N. E. Clarke [2004], A game of cops and robber played with partial information, Proceedings of the Thirty-Fifth Southeastern International Conference on Combinatorics, Graph Theory and Computing, Vol. 166, pp. 145–159, 2122009 (2006f:05152).

383. N. E. Clarke [2009], A witness version of the cops and robber game, Discrete Math. 309, 3292–3298, 2526747 (2011a:91080).

http://dx.doi.org/10.1016/j.disc.2008.09.032

384. N. E. Clarke and E. L. Connon [2006], Cops, robber, and alarms, Ars Combin. 81, 283–296, 2267819 (2007k:91049).

385. N. E. Clarke, S. L. Fitzpatrick, A. Hill and R. J. Nowakowski [2010], Edge critical cops and robber, Discrete Math. 310, 2299–2309, 2659181 (2011k:05057).

http://dx.doi.org/10.1016/j.disc.2010.05.004

386. T. A. Clarke, R. A. Hochberg and G. H. Hurlbert [1997], Pebbling in diameter two graphs and products of paths, J. Graph Theory 25, 119– 128.

387. N. E. Clarke and R. J. Nowakowski [2000], Cops, robber, and photo radar, Ars Combin. 56, 97–103, MR1768605 (2001e:91040).

388. N. E. Clarke and R. J. Nowakowski [2001], Cops, robber and traps, Util. Math. 60, 91–98, MR1863432 (2002i:91014).

389. N. E. Clarke and R. J. Nowakowski [2005], A tandem version of the cops and robber game played on products of graphs, Discuss. Math. Graph Theory 25(3), 241–249, 2232750 (2007f:05170).

390. N. E. Clarke and R. J. Nowakowski [2005], Tandem-win graphs, Discrete Math. 299, 56–64, MR2168695.

391. N. Claus (=E. Lucas) [1884], La tour d’Hanoi, jeu de calcul, Science et Nature 1, 127–128.

392. A. Clausing [2001], Das Trisentis Spiel (The Trisentis game), Math. Semesterberichte 48, 49–66, MR1950212 (2003k:91045).

393. E. J. Cockayne [1990], Chessboard domination problems, Discrete Math. 86, 13–20.

394. E. J. Cockayne and S. T. Hedetniemi [1986], On the diagonal queens domination problem, J. Combin. Theory (Ser. A) 42, 137–139.

395. E. J. Cockayne and C. M. Mynhardt [2001], Properties of queens graphs and the irredundance number of Q_{7}, Australas. J. Combin. 23, 285–299, MR1815019 (2002a:05189).

396. A. J. Cole and A. J. T. Davie [1969], A game based on the Euclidean algorithm and a winning strategy for it, Math. Gaz. 53, 354–357.

397. D. B. Coleman [1978], Stretch: a geoboard game, Math. Mag. 51, 49–54.

398. S. Collette, E. D. Demaine, M. L. Demaine and S. Langerman [2013], Narrow Misère Dots-and-Boxes, in: Games of No Chance 4 , Cambridge University Press, to appear.

399. D. Collins [2005], Variations on a theme of Euclid, Integers, Electr. J. of Combinat. Number Theory 5, #G3, 12 pp., Comb. Games Sect., MR2139166 (2005k:91080).

http://www.integers-ejcnt.org/vol5.html

400. D. Collins and T. Lengyel [2008], The game of 3-Euclid, Discrete Math. 308(7), 1130–1136, 2382351 (2008k:91050).

http://dx.doi.org/10.1016/j.disc.2007.03.064

401. A. Condon [1989], Computational Models of Games, ACM Distinguished Dissertation, MIT Press, Cambridge, MA.

402. A. Condon [1991], Space-bounded probabilistic game automata, J. Assoc. Comput. Mach. 38, 472–494.

403. A. Condon [1992], The complexity of Stochastic games, Information and Computation 96, 203–224.

404. A. Condon [1993], On algorithms for simple stochastic games, in: Advances in Computational Complexity Theory (New Brunswick, NJ, 1990), DIMACS Ser. Discrete Math. Theoret. Comput. Sci., Vol. 13, Amer. Math. Soc., Providence, RI, pp. 51–71.

405. A. Condon, J. Feigenbaum, C. Lund and P. Shor [1993], Probabilistically checkable debate systems and approximation algorithms for PSPACEhard functions, Proc. 25th Ann. ACM Symp. Theory of Computing, Assoc. Comput. Mach., New York, NY, pp. 305–314.

406. A. Condon and R. E. Ladner [1988], Probabilistic game automata, J. Comput. System Sci. 36, 452–489, preliminary version in: Proc. Structure in complexity theory (Berkeley, CA, 1986), Lecture Notes in Comput. Sci., Vol. 223, Springer, Berlin, pp. 144–162.

407. I. G. Connell [1959], A generalization of Wythoff’s game, Canad. Math. Bull. 2, 181–190, MR0109092 (21 #7804).

408. I. G. Connell [1959], Some properties of Beatty sequences I, Canad. Math. Bull. 2, 190–197, MR0109093 (21 #7805).

409. I. G. Connell [1960], Some propertis of Beatty squences. II, Canad. Math. Bull. 3, 17–22, 0110683 (22 #1558).

410. J. H. Conway [1972], All numbers great and small, Res. Paper No. 149, Univ. of Calgary Math. Dept.

411. J. H. Conway [1977], All games bright and beautiful, Amer. Math. Monthly 84, 417–434.

412. J. H. Conway [1978], A gamut of game theories, Math. Mag. 51, 5–12.

413. J. H. Conway [1978], Loopy Games, Ann. Discrete Math. 3, 55–74, Proc. Symp. Advances in Graph Theory, Cambridge Combinatorial Conf. (B. Bollobás, ed.), Cambridge, May 1977.

414. J. H. Conway [1990], Integral lexicographic codes, Discrete Math. 83, 219–235.

415. J. H. Conway [1991], More ways of combining games, in: Combinatorial Games, Proc. Symp. Appl. Math. (R. K. Guy, ed.), Vol. 43, Amer. Math. Soc., Providence, RI, pp. 57–71.

416. J. H. Conway [1991], Numbers and games, in: Combinatorial Games, Proc. Symp. Appl. Math. (R. K. Guy, ed.), Vol. 43, Amer. Math. Soc., Providence, RI, pp. 23–34.

417. J. H. Conway [1994], The surreals and the reals. Real numbers, generalizations of the reals, and theories of continua, in: Synthese Lib., Vol. 242, Kluwer Acad. Publ., Dordrecht, pp. 93–103.

418. J. H. Conway [1996], The angel problem, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 3–12.

419. J. H. Conway [1997], M_{13}, in: Surveys in combinatorics, London Math. Soc., Lecture Note Ser. 241, Cambridge Univ. Press, Cambridge, pp. 1–11.

420. J. H. Conway [2001], On Numbers and Games, A K Peters, Natick, MA, 2nd edition; translation of 1st edition (1976) into German: Über Zahlen und Spiele by Brigitte Kunisch, Friedr. Vieweg & Sohn, Braunschweig, 1983.

421. J. H. Conway [2002], More infinite games, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 31–36, MR1973002.

422. J. H. Conway [2003], Integral lexicographic codes, in: MASS selecta (S. Katok and S. Tabachnikov, eds.), Amer. Math. Soc., pp. 185–189, MR2027176.

423. J. H. Conway and H. S. M. Coxeter [1973], Triangulated polygons and frieze patterns, Math. Gaz. 57, 87–94; 175–183.

424. J. H. Conway and N. J. A. Sloane [1986], Lexicographic codes: errorcorrecting codes from game theory, IEEE Trans. Inform. Theory IT-32, 337–348.

425. M. L. Cook and L. E. Shader [1979], A strategy for the Ramsey game “TRITIP”, Congr. Numer. 23, 315–324, Utilitas Math., Proc. 10th Southeastern Conf. on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1979), MR561058 (83e:90167).

426. M. Copper [1993], Graph theory and the game of sprouts, Amer. Math. Monthly 100, 478–482.

427. M. Cornelius and A. Parr [1991], What’s Your Game?, Cambridge University Press, Cambridge.

428. T. Cover [1987], Pick the largest number, Open Problems in Communication and Computation (T. M. Cover and B. Gopinath, eds.), Springer-Verlag, New York, p. 152.

429. H. S. M. Coxeter [1953], The golden section, phyllotaxis and Wythoff’s game, Scripta Math. 19, 135–143.

430. D. Craft, Z. Miller and D. Pritikin [2009], A solitaire game played on 2-colored graphs, Discrete Math. 309, 188–201, 2475010 (2010a:91030).

http://dx.doi.org/10.1016/j.disc.2007.12.069

431. M. Crâşmaru [2001], On the complexity of Tsume-Go, Proc. Intern. Conference on Computers and Games CG’1998, Tsukuba, Japan, Nov. 1998 (H. J. van den Herik, ed.), Vol. LNCS 1558, Lecture Notes in Computer Science, Springer, pp. 222–231.

432. M. Crâşmaru and J. Tromp [2001], Ladders are PSPACE-complete, Proc. 2nd Intern. Conference on Computers and Games CG’2000 (T. Marsland and I. Frank, eds.), Vol. 2063, Hamamatsu, Japan, Oct. 2000, Lecture Notes in Computer Science, Springer, pp. 241–249, MR1909613.

433. J. W. Creely [1987], The length of a two-number game, Fibonacci Quart. 25, 174–179.

434. J. W. Creely [1988], The length of a three-number game, Fibonacci Quart. 26, 141–143.

435. H. T. Croft [1964], ‘Lion and man’: a postscript, J. London Math. Soc. 39, 385–390.

436. D. W. Crowe [1956], The n-dimensional cube and the tower of Hanoi, Amer. Math. Monthly 63, 29–30.

437. B. Crull, T. Cundiff, P. Feltman, G. H. Hurlbert, L. Pudwell, Z. Szaniszlo and Z. Tuza [2005], The cover pebbling number of graphs, Discrete Math. 296, 15–23, MR2148478.

438. A. Csernenszky, C. I. Mándity and A. Pluhár [2009], On Chooser-Picker positional games, Discrete Math. 309, 5141–5146, 2548915 (2011e:05171).

http://dx.doi.org/10.1016/j.disc.2009.03.051

439. A. Csernenszky, R. R. Martin and A. Pluhár [2011], On the complexity of chooser-picker positional games, Integers, Electr. J. of Combinat. Number Theory 11, #G02, 16 pp., Comb. Games Sect.

http://www.integers-ejcnt.org/vol11.html

440. L. Csirmaz [1980], On a combinatorial game with an application to Gomoku, Discrete Math. 29(1), 19–23, 553645 (81a:05013).

http://dx.doi.org/10.1016/0012-365X(90)90282-M

441. L. Csirmaz [2002], Connected graph game, Studia Sci. Math. Hungar. 39, 129–136, MR1909151 (2003d:91028).

442. L. Csirmaz and Z. Nagy [1979], On a generalization of the game Go-Moku II, Studia Sci. Math. Hung. 14, 461–469.

443. P. Csorba [2005], On the biased n-in-a-row game, Discrete Math. 503, 100–111.

444. J. Culberson [1999], Sokoban is PSPACE complete, in: Fun With Algorithms, Vol. 4 of Proceedings in Informatics, Carleton Scientific, University of Waterloo, Waterloo, Ont., pp. 65–76, Conference took place on the island of Elba, June 1998.

445. P. Cull and E. F. Ecklund, Jr. [1982], On the towers of Hanoi and generalized towers of Hanoi problems, Congr. Numer. 35, 229–238.

446. P. Cull and E. F. Ecklund, Jr. [1985], Towers of Hanoi and analysis of algorithms, Amer. Math. Monthly 92, 407–420.

447. P. Cull and C. Gerety [1985], Is towers of Hanoi really hard?, Congr. Numer. 47, 237–242.

448. P. Cull and I. Nelson [1999], Error-correcting codes on the towers of Hanoi graphs, Discrete Math. 208/209, 157–175.

449. P. Cull and I. Nelson [1999], Perfect codes, NP-completeness, and towers of Hanoi graphs, Bull. Inst. Combin. Appl. 26, 13–38.

450. D. Curtis, T. Hines, G. Hurlbert and T. Moyer [2009], On pebbling graphs by their blocks, Integers 9, G02, 411–422, 2592545 (2011b:05169).

http://dx.doi.org/10.1515/INTEG.2009.033

451. A. Czygrinow, N. Eaton, G. Hurlbert and P. M. Kayll [2002], On pebbling threshold functions for graph sequences, Discrete Math. 247, 93– 105, MR1877652 (2002m:05058).

452. A. Czygrinow and G.Hurlbert [2003], Pebbling in dense graphs, Australas. J. Combin. 28, 201–208.

453. A. Czygrinow, G. Hurlbert, H. A. Kierstead and W. T. Trotter [2002], A note on graph pebbling, Graphs Combin. 18, 219–225, MR1913664 (2004d:05170).

454. J. Czyzowicz, K. B. Lakshmanan and A. Pelc [1991], Searching with a forbidden lie pattern in responses, Inform. Process. Lett. 37, 127–132, MR1095694 (92e:68027).

455. J. Czyzowicz, K. B. Lakshmanan and A. Pelc [1994], Searching with local constraints on error patterns, European J. Combin. 15, 217–222, MR1273940 (95a:05005).

456. J. Czyzowicz, D. Mundici and A. Pelc [1989], Ulam’s searching game with lies, J. Combin. Theory Ser. A 52, 62–76, MR1008160 (90k:94026).

457. J. Czyzowicz, A. Pelc and D. Mundici [1988], Solution of Ulam’s problem on binary search with two lies, J. Combin. Theory Ser. A 49, 384–388, MR964397 (90k:94025).

458. G. Danaraj and V. Klee [1977], The connectedness game and the c-comp-lexity of certain graphs, SIAM J. Appl. Math. 32, 431–442.

459. C. Darby and R. Laver [1998], Countable length Ramsey games, Set Theory: Techniques and Applications. Proc. of the conferences, Curacao, Netherlands Antilles, June 26–30, 1995 and Barcelona, Spain, June 10–14, 1996 (C. A. Di Prisco et al., eds.), Kluwer, Dordrecht, pp. 41–46.

460. C. Daskalakis, P. W. Goldberg and C. H. Papadimitriou [2009], The complexity of computing a Nash equilibrium, SIAM J. Comput. 39(1), 195– 259, 2506524 (2010e:91006).

http://dx.doi.org/10.1137/070699652

461. C. Daskalakis, A. Mehta and C. Papadimitriou [2009], A note on approximate Nash equilibria, Theoret. Comput. Sci. 410(17), 1581–1588, 2510264 (2010g:68303).

http://dx.doi.org/10.1016/j.tcs.2008.12.031

462. A. L. Davies [1970], Rotating the fifteen puzzle, Math. Gaz. 54, 237–240.

463. M. Davis [1963], Infinite games of perfect information, Ann. of Math. Stud., Princeton 52, 85–101.

464. R. W. Dawes [1992], Some pursuit-evasion problems on grids, Inform. Process. Lett. 43, 241–247.

465. T. R. Dawson [1934], Problem 1603, Fairy Chess Review p. 94, Dec.

466. T. R. Dawson [1935], Caissa’s Wild Roses, reprinted in: Five Classics of Fairy Chess, Dover, 1973.

467. N. G. de Bruijn [1972], A solitaire game and its relation to a finite field, J. Recr. Math. 5, 133–137.

468. N. G. de Bruijn [1981], Pretzel Solitaire as a pastime for the lonely mathematician, in: The Mathematical Gardner (D. A. Klarner, ed.), Wadsworth Internat., Belmont, CA, pp. 16–24.

469. F. de Carteblanche [1970], The princess and the roses, J. Recr. Math. 3, 238–239.

470. F. deCarte Blanche [1974], The roses and the princes, J. Recr. Math. 7, 295–298.

471. A. P. DeLoach [1971], Some investigations into the game of SIM, J. Recr. Math. 4, 36–41.

472. E. D. Demaine [2001], Playing games with algorithms: algorithmic combinatorial game theory, Mathematical Foundations of Computer Science (J. Sgall, A. Pultr and P. Kolman, eds.), Vol. 2136 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 18–32, MR1906998 (2003d:68076).

473. E. D. Demaine, M. L. Demaine and D. Eppstein [2002], Phutball Endgames are Hard, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 351–360, MR1973023 (2004b:91042).

474. E. D. Demaine, M. L. Demaine and R. Fleischer [2004], Solitaire clobber, Theoret. Comp. Sci. 313, 325–338, special issue of Dagstuhl Seminar “Algorithmic Combinatorial Game Theory”, Feb. 2002, MR2056930.

475. E. D. Demaine, M. L. Demaine, R. Fleischer, R. A. Hearn and T. von Oertzen [2009], The complexity of the Dyson Telescopes puzzle, in: Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 271–285.

476. E. Demaine, M. L. Demaine and J. O’Rourke [2000], PushPush and Push-1 are NP-hard in 2D, Proc. 12th Annual Canadian Conf. on Computational Geometry, Fredericton, New Brunswick, Canada, pp. 17–20.

477. E. D. Demaine, M. L. Demaine and H. A. Verrill [2002], Coin-moving puzzles, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 405–431, MR1973108 (2004b:91043).

478. E. D. Demaine, R. Fleischer, A. Fraenkel and R. J. Nowakowski [2004], Appendix B: Open problems at the 2002 Dagstuhl Seminar on Algorithmic Combinatorial Game Theory, Theoret. Comput. Sci. 313(3), 539–543, Algorithmic combinatorial game theory, 2056945.

http://dx.doi.org/10.1016/j.tcs.2003.09.012

479. E. D. Demaine and R. A. Hearn [2008], Constraint logic: a uniform framework for modeling computation as games, in: Twenty-Third Annual IEEE Conference on Computational Complexity, IEEE Computer Soc., Los Alamitos, CA, pp. 149–162, 2513497 (2010d:68039).

http://dx.doi.org/10.1109/CCC.2008.35

480. E. D. Demaine and R. A. Hearn [2009], Playing games with algorithms: algorithmic combinatorial game theory, in: Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 3–56, an updated version of E.D. Demaine’s paper of the same title, 2001.

481. E. D. Demaine, R. A. Hearn and M. Hoffmann [2002], Push-2-f is PSPACE-Complete, Proc. 14th Canad. Conf. Computational Geometry, Lethbridge, Alberta, Canada, pp. 31–35.

482. J. DeMaio [2007], Which chessboards have a closed knight’s tour within the cube?, Electr. J. Combin. 14, #R32, 9 pp.

http://www.combinatorics.org/

483. J. DeMaio and B. Mathew [2011], Which chessboards have a closed knight’s tour within the rectangular prism?, Electron. J. Combin. 18(1), Paper 8, 14, 2770113 (2012d:05210).

484. H. de Parville [1884], La tour d’Hanoï et la question du Tonkin, La Nature 12, 285–286.

485. C. Deppe [2000], Solution of Ulam’s searching game with three lies or an optimal adaptive strategy for binary three-error-correcting codes, Discrete Math. 224, 79–98, MR1781286 (2001j:94054).

486. C. Deppe [2004], Strategies for the Renyi-Ulam game with fixed number of lies, Theoret. Comput. Sci. 314, 45–55, MR2033744 (2004k:05012).

487. D. Dereniowski [2010], Phutball is PSPACE-hard, Theoret. Comput. Sci. 411, 3971–3978, 2768776 (2011h:91056).

http://dx.doi.org/10.1016/j.tcs.2010.08.019

488. D. Dereniowski [2011], The complexity of node blocking for dags, J. Combin. Theory Ser. A 118, 248–256, 2737198.

http://dx.doi.org/10.1016/j.jcta.2010.03.011

489. B. Descartes [1953], Why are series musical?, Eureka 16, 18–20, reprinted ibid. 27 (1964) 29–31.

490. W. Deuber and S. Thomassé [1996], Grundy Sets of Partial Orders, Technical Report No. 96-123 , Diskrete Strukturen in der Mathematik, Universität Bielefeld.

491. M. Develin and S. Payne [2010], Discrete bidding games, Electron. J. Combin. 17(1), Research Paper 85, 40, 2661388 (2011j:91062).

http://www.combinatorics.org/Volume_17/Abstracts/v17i1r85.
html

492. A. K. Dewdney [1984 – 1991 ], Computer Recreations, a column in Scientific American (May, 1984 – September 1991).

493. A. K. Dewdney [1988], The Armchair Universe: An Exploration of Computer Worlds, W. H. Freeman and Company, New York.

494. A. K. Dewdney [1989], The Turing Omnibus: 61 Excursions in Computer Science, Computer Science Press, Rockville, MD.

495. A. K. Dewdney [1993], The (new) Turing Omnibus: 66 Excursions in Computer Science, Computer Science Press, New York.

496. A. Deza and S. Onn [1999], Odd central square solitaire, Sūrikaisekikenkyūsho Kōkyūroku (1114), 96–105, Continuous and discrete mathematics for optimization (Kyoto, 1999), 1767317.

497. A. Deza and S. Onn [2002], Solitaire lattices, Graphs Combin. 18(2), 227– 243, 1913665 (2003d:05021).

http://dx.doi.org/10.1007/s003730200016

498. A. Dhagat, P. Gács and P. Winkler [1992], On playing ”twenty questions” with a liar, Proc. Third Annual ACM-SIAM Sympos. on Discrete Algorithms, (Orlando, FL, 1992), ACM, New York, pp. 16–22.

499. C. S. Dibley and W. D. Wallis [1981], The effect of starting position in jai-alai, Congr. Numer. 32, 253–259, Proc. 12-th Southeastern Conf. on Combinatorics, Graph Theory and Computing, Vol. I (Baton Rouge, LA, 1981).

500. C. G. Diderich [1995], Bibliography on minimax game theory, sequential and parallel algorithms.

http://diwww.epfl.ch/$\sim$diderich/bibliographies.html

501. R. Diestel and I. Leader [1994], Domination games on infinite graphs, Theoret. Comput. Sci. (Math Games) 132, 337–345.

502. T. Dinski and X. Zhu [1999], A bound for the game chromatic number of graphs, Discrete Math. 196(1-3), 109–115, MR1664506 (99k:05077).

503. Y. Dodis and P. Winkler [2001], Universal configurations in light-flipping games, Proc. 12th Annual ACM-SIAM Sympos. on Discrete Algorithms, (Washington, DC, 2001), ACM, New York, pp. 926–927.

504. B. Doerr [2001], Vector balancing games with aging, J. Combin. Theory Ser. A 95(2), 219–233, 1845142 (2002f:91018).

http://dx.doi.org/10.1006/jcta.2000.3163

505. A. P. Domoryad [1964], Mathematical Games and Pastimes, Pergamon Press, Oxford, translated by H. Moss.

506. R. G. Donnelly [2008], Eriksson’s numbers game and finite Coxeter groups, European J. Combin. 29(7), 1764–1781, 2431767 (2009d:05259).

http://dx.doi.org/10.1016/j.ejc.2007.06.029

507. D. Dor and U. Zwick [1999], SOKOBAN and other motion planning problems, Comput. Geom. 13, 215–228.

508. P. Dorbec, E. Duchêne and S. Gravier [2008], Solitaire Clobber played on Hamming graphs, Integers, Electr. J of Combinat. Number Theory 8, G3, 21, MR2393376 (2009b:91037).

509. I. Douglas and N. Sieben [2012], Edge animal weak (1, 2)-achievement games, Integers, Electr. J of Combinat. Number Theory 12, G5, 13.

510. M. Dresher [1951], Games of strategy, Math. Mag. 25, 93–99.

511. A. Dress, A. Flammenkamp and N. Pink [1999], Additive periodicity of the Sprague-Grundy function of certain Nim games, Adv. in Appl. Math. 22, 249–270.

512. G. C. Drummond-Cole [2005], Positions of value ^{∗}2 in generalized domineering and chess, Integers 5(1), G6, 13, 2192254 (2006g:11043).

513. Y. Du [2008], On the complexity of deciding bimatrix games similarity, Theoret. Comput. Sci. 407(1-3), 583–586, 2463040 (2010g:91008).

http://dx.doi.org/10.1016/j.tcs.2008.07.021

514. E. Duchêne, A. S. Fraenkel, S. Gravier and R. J. Nowakowski [2009], Another bridge between NIM and WYTHOFF, Australas. J. Combin. 44, 43–56, 2526997 (2010h:91056).

515. E. Duchêne, A. S. Fraenkel, R. J. Nowakowski and M. Rigo [2010], Extensions and restrictions of Wythoff’s game preserving its P positions, J. Combin. Theory Ser. A 117(5), 545–567, 2600974 (2011d:91073).

http://dx.doi.org/10.1016/j.jcta.2009.07.010

516. E. Duchêne and S. Gravier [2009], Geometrical extensions of Wythoff’s game, Discrete Math. 309, 3595–3608, 2528073 (2010k:91051).

http://dx.doi.org/10.1016/j.disc.2007.12.089

517. E. Duchêne, S. Gravier and M. Mhalla [2009], Combinatorial graph games, Ars Combin. 90, 33–44, 2473164 (2010b:05123).

518. E. Duchêne, S. Gravier and J. Moncel [2009], New results about impartial solitaire clobber, RAIRO Oper. Res. 43, 463–482, 2573994 (2011b:91079).

http://dx.doi.org/10.1051/ro/2009029

519. E. Duchêne and M. Rigo [2008], A morphic approach to combinatorial games: the Tribonacci case, Theor. Inform. Appl. 42(2), 375–393, 2401268 (2009b:91038).

http://dx.doi.org/10.1051/ita:2007039

520. E. Duchêne and M. Rigo [2008], Cubic Pisot unit combinatorial games, Monatsh. Math. 155(3-4), 217–249, 2461578 (2009m:68199).

http://dx.doi.org/10.1007/s00605-008-0006-x

521. E. Duchêne and M. Rigo [2010], Invariant games, Theoret. Comput. Sci. 411, 3169–3180, 2676861 (2011i:91038).

http://dx.doi.org/10.1016/j.tcs.2010.05.007

522. P. Duchet [1980], Graphes noyau-parfaits, Ann. Discrete Math. 9, 93–101.

523. P. Duchet [1987], A sufficient condition for a digraph to be kernel-perfect, J. Graph Theory 11, 81–85.

524. P. Duchet [1987], Parity graphs are kernel-M-solvable, J. Combin. Theory (Ser. B) 43, 121–126.

525. P. Duchet and H. Meyniel [1981], A note on kernel-critical graphs, Discrete Math. 33, 103–105.

526. P. Duchet and H. Meyniel [1983], Une généralisation du théorème de Richardson sur l’existence de noyaux dans le graphes orientés, Discrete Math. 43, 21–27.

527. P. Duchet and H. Meyniel [1993], Kernels in directed graphs: a poison game, Discrete Math. 115, 273–276.

528. H. E. Dudeney [1958], The Canterbury Puzzles and Other Curious Problems, Dover, Mineola, NY, 4th edn., 1st edn: W. Heinemann, 1907.

529. H. E. Dudeney [1970], Amusements in Mathematics, Dover, Mineola, NY, 1st edn: Dover, 1917, reprinted by Dover in 1959.

530. A. Duffy, G. Kolpin and D. Wolfe [2009], Ordinal partizan End Nim, in: Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 419–425.

531. I. Dumitriu and J. Spencer [2004], A halfliar’s game, Theoret. Comp. Sci. 313, 353–369, special issue of Dagstuhl Seminar “Algorithmic Combinatorial Game Theory”, Feb. 2002, MR2056932.

532. I. Dumitriu and J. Spencer [2005], The liar game over an arbitrary channel, Combinatorica 25(5), 537–559, MR2176424 (2006m:91003).

533. I. Dumitriu and J. Spencer [2005], The two-batch liar game over an arbitrary channel, SIAM J. Discrete Math. 19(4), 1056–1064 (electronic), MR2206379 (2006m:91037).

534. C. Dunn [2007], The relaxed game chromatic index of k-degenerate graphs, Discrete Math. 307(14), 1767–1775, MR2316815 (2007m:05085).

535. C. Dunn and H. A. Kierstead [2004], A simple competitive graph coloring algorithm. II, J. Combin. Theory Ser. B 90(1), 93–106, Dedicated to Adrian Bondy and U. S. R. Murty, MR2041319 (2005h:05072).

536. C. Dunn and H. A. Kierstead [2004], A simple competitive graph coloring algorithm. III, J. Combin. Theory Ser. B 92(1), 137–150, MR2078498 (2007b:05069).

537. C. Dunn and H. A. Kierstead [2004], The relaxed game chromatic number of outerplanar graphs, J. Graph Theory 46(1), 69–78, MR2051470 (2004m:05097).

538. N. Duvdevani and A. S. Fraenkel [1989], Properties of k-Welter’s game, Discrete Math. 76(3), 197–221, 1009869 (91a:90182).

http://dx.doi.org/10.1016/0012-365X(89)90320-8

539. S. Dyrkolbotn and M. Walicki [2012], Kernels in digraphs that are not kernel perfect, Discrete Math. 312, 2498–2505.

540. J. Edmonds [1965], Lehman’s switching game and a theorem of Tutte and Nash–Williams, J. Res. Nat. Bur. Standards 69B, 73–77.

541. B. Effantin and H. Kheddouci [2007], Grundy number of graphs, Discuss. Math. Graph Theory 27(1), 5–18, 2321417 (2008a:05089).

http://dx.doi.org/10.7151/dmgt.1339

542. R. Ehrenborg and E. Steingrímsson [1996], Playing Nim on a simplicial complex, Electron. J. Combin. 3(1), Research Paper 9, approx. 33 pp. (electronic), 1376659 (97c:90158).

http://www.combinatorics.org/Volume_3/Abstracts/v3i1r9.html

543. A. Ehrenfeucht and J. Mycielski [1979], Positional strategies for mean payoff games, Internat. J. Game Theory 8, 109–113.

544. N. D. Elkies [1996], On numbers and endgames: combinatorial game theory in chess endgames, in: Games of no chance (Berkeley, CA, 1994), Vol. 29 of Math. Sci. Res. Inst. Publ., Cambridge Univ. Press, Cambridge, pp. 135–150, 1427963.

545. N. D. Elkies [2002], Higher nimbers in pawn endgames on large chessboards, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 61–78, MR1973005 (2004c:91029).

546. N. D. Elkies [2004/06], New directions in enumerative chess problems, Electron. J. Combin. 11(2), Article 4, 14 pp. (electronic), 2195435 (2006i:05004).

http://www.combinatorics.org/Volume_11/Abstracts/v11i2a4.
html

547. N. D. Elkies and R. P. Stanley [2003], The mathematical knight, Math. Intelligencer 25(1), 22–34, 1962924 (2004c:05113).

http://dx.doi.org/10.1007/BF02985635

548. R. B. Ellis and K. L. Nyman [2009], Two-batch liar games on a general bounded channel, J. Combin. Theory Ser. A 116(8), 1253–1270, 2568798 (2011j:91054).

http://dx.doi.org/10.1016/j.jcta.2009.03.005

549. R. B. Ellis, V. Ponomarenko and C. H. Yan [2005], The Rényi-Ulam pathological liar game with a fixed number of lies, J. Combin. Theory Ser. A 112, 328–336, MR2177490 (2006g:91040).

550. R. B. Ellis and C. H. Yan [2004], Ulam’s pathological liar game with one half-lie, Int. J. Math. Math. Sci. pp. 1523–1532, MR2085073 (2005c:91033).

551. J. W. Emert, R. B. Nelson and F. W. Owens [2007], Multiple towes of Hanoi with a path transition graph, Congr. Numer. 188, 59–64, Proc. 38-th Southeastern Intern. Conf. on Combinatorics, Graph Theory and Computing (Boca Raton, Fl, 2007).

552. D. Engel [1972], DIM: three-dimensional Sim, J. Recr. Math. 5, 274–275.

553. M. R. Engelhardt [2007], A group-based search for solutions of the n-queens problem, Discrete Math. 307, 2535–2551, MR2359600 (2008g:05204).

554. B. Engels and T. Kamphans [2006], Randolph’s robot game is NP-hard!, in: CTW2006—Cologne-Twente Workshop on Graphs and Combinatorial Optimization, Vol. 25 of Electron. Notes Discrete Math., Elsevier, Amsterdam, pp. 49–53 (electronic), MR2301136.

555. R. J. Epp and T. S. Ferguson [1980], A note on take-away games, Fibonacci Quart. 18, 300–303.

556. D. Eppstein [2002], Searching for spaceships, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 433–453.

557. R. A. Epstein [1977], Theory of Gambling and Statistial Logic, Academic Press, New York, NY.

558. M. C. Er [1982], A representation approach to the tower of Hanoi problem, Comput. J. 25, 442–447.

559. M. C. Er [1983], An analysis of the generalized towers of Hanoi problem, BIT 23, 429–435.

560. M. C. Er [1983], An iterative solution to the generalized towers of Hanoi problem, BIT 23, 295–302.

561. M. C. Er [1984], A generalization of the cyclic towers of Hanoi, Intern. J. Comput. Math. 15, 129–140.

562. M. C. Er [1984], The colour towers of Hanoi: a generalization, Comput. J. 27, 80–82.

563. M. C. Er [1984], The cyclic towers of Hanoi: a representation approach, Comput. J. 27, 171–175.

564. M. C. Er [1984], The generalized colour towers of Hanoi: an iterative algorithm, Comput. J. 27, 278–282.

565. M. C. Er [1984], The generalized towers of Hanoi problem, J. Inform. Optim. Sci. 5, 89–94.

566. M. C. Er [1985], The complexity of the generalized cyclic towers of Hanoi problem, J. Algorithms 6, 351–358.

567. M. C. Er [1987], A general algorithm for finding a shortest path between two n-configurations, Information Sciences 42, 137–141.

568. M. C. Er [1987], A time and space efficient algorithm for the cyclic Towers of Hanoi problem, J. Inform. Process. 9, 163–165.

569. M. C. Er [1988], A minimal space algorithm for solving the towers of Hanoi problem, J. Inform. Optim. Sci. 9, 183–191.

570. M. C. Er [1989], A linear space algorithm for solving the Towers of Hanoi problem by using a virtual disc., Inform. Sci. 47, 47–52.

571. C. Erbas, S. Sarkeshik and M. M. Tanik [1992], Different perspectives of the N-queens problem, Proc. ACM Computer Science Conf., Kansas City, MO, pp. 99–108.

572. C. Erbas and M. M. Tanik [1994], Parallel memory allocation and data alignment in SIMD machines, Parallel Algorithms and Applications 4, 139–151, preliminary version appeared under the title: Storage schemes for parallel memory systems and the N-queens problem, in: Proc. 15th Ann. Energy Tech. Conf., Houston, TX, Amer. Soc. Mech. Eng., Vol. 43, 1992, pp. 115–120.

573. C. Erbas, M. M. Tanik and Z. Aliyazicioglu [1992], Linear conguence equations for the solutions of the N-queens problem, Inform. Process. Lett. 41, 301–306.

574. J. Erde [1989], The closed knight tour problem in higher dimensions, Electron. J. Combin. 19(4), #P9, 17 pp. (electronic).

575. P. Erdős, W. R. Hare, S. T. Hedetniemi and R. C. Laskar [1987], On the equality of the Grundy and ochromatic numbers of a graph, J. Graph Theory 11, 157–159.

576. P. Erdős, S. T. Hedetniemi, R. C. Laskar and G. C. E. Prins [2003], On the equality of the partial Grundy and upper ochromatic numbers of graphs, Discrete Math. 272, 53–64, MR2019200 (2004i:05048).

577. P. Erdős and J. L. Selfridge [1973], On a combinatorial game, J. Combinatorial Theory Ser. A 14, 298–301, 0327313 (48 #5655).

578. P. L. Erdös, U. Faigle, W. Hochstättler and W. Kern [2004], Note on the game chromatic index of trees, Theoret. Comp. Sci. 313, 371–376, special issue of Dagstuhl Seminar “Algorithmic Combinatorial Game Theory”, Feb. 2002, MR2056933.

579. P. L. Erdős and L. Soukup [2009], Quasi-kernels and quasi-sinks in infinite graphs, Discrete Math. 309(10), 3040–3048, 2526721 (2010i:05243).

http://dx.doi.org/10.1016/j.disc.2008.08.006

580. J. Erickson [1996], New toads and frogs results, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 299–310.

581. J. Erickson [1996], Sowing games, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 287–297.

582. M. Erickson and F. Harary [1983], Picasso animal achievement games, Bull. Malaysian Math. Soc. 6, 37–44.

583. N. Eriksen, H. Eriksson and K. Eriksson [2000], Diagonal checker-jumping and Eulerian numbers for color-signed permutations, Electr. J. Combin. 7, #R3, 11 pp.

http://www.combinatorics.org/

584. H. Eriksson [1995], Pebblings, Electr. J. Combin. 2, #R7, 18 pp.

http://www.combinatorics.org/

585. H. Eriksson, K. Eriksson, J. Karlander, L. Svensson and J. Wästlund [2001], Sorting a bridge hand, Discrete Math. 241, 289–300, Selected papers in honor of Helge Tverberg.

586. H. Eriksson, K. Eriksson and J. Sjöstrand [2001], Note on the lamp lighting problem, Adv. in Appl. Math. 27, 357–366, Special issue in honor of Dominique Foata’s 65th birthday (Philadelphia, PA, 2000), MR1868970 (2002i:68082).

587. H. Eriksson and B. Lindström [1995], Twin jumping checkers in Z^{d}, European J. Combin. 16, 153–157, 1324425 (96c:05011).

http://dx.doi.org/10.1016/0195-6698(95)90054-3

588. K. Eriksson [1991], No polynomial bound for the chip firing game on directed graphs, Proc. Amer. Math. Soc. 112(4), 1203–1205, 1065944 (91j:90110).

http://dx.doi.org/10.2307/2048674

589. K. Eriksson [1992], Convergence of Mozes’s game of numbers, Linear Algebra Appl. 166, 151–165, 1152492 (92m:90073).

http://dx.doi.org/10.1016/0024-3795(92)90274-E

590. K. Eriksson [1994], Node firing games on graphs, in: Jerusalem combinatorics ’93 , Vol. 178 of Contemp. Math., Amer. Math. Soc., Providence, RI, pp. 117–127, 1310579 (95i:90129).

http://dx.doi.org/10.1090/conm/178/01896

591. K. Eriksson [1994], Reachability is decidable in the numbers game, Theoret. Comput. Sci. 131(2), 431–439, 1288949 (95i:90122).

http://dx.doi.org/10.1016/0304-3975(94)90182-1

592. K. Eriksson [1995], The numbers game and Coxeter groups, Discrete Math. 139(1-3), 155–166, Formal power series and algebraic combinatorics (Montreal, PQ, 1992), 1336838 (96f:05184).

http://dx.doi.org/10.1016/0012-365X(94)00131-2

593. K. Eriksson [1996], Chip-firing games on mutating graphs, SIAM J. Discrete Math. 9(1), 118–128, 1375419 (97c:90160).

http://dx.doi.org/10.1137/S0895480192240287

594. K. Eriksson [1996], Strong convergence and a game of numbers, European J. Combin. 17(4), 379–390, 1387469 (97d:05267).

http://dx.doi.org/10.1006/eujc.1996.0031

595. K. Eriksson [1996], Strong convergence and the polygon property of 1player games, Proceedings of the 5th Conference on Formal Power Series and Algebraic Combinatorics (Florence, 1993), Vol. 153, pp. 105–122, 1394949 (97d:90132).

http://dx.doi.org/10.1016/0012-365X(95)00131-F

596. M. D. Ernst [1995], Playing Konane mathematically: a combinatorial game-theoretic analysis, UMAP J. 16(2), 95–121, MR1439041.

597. L. Esperet and X. Zhu [2009], Game colouring of the square of graphs, Discrete Math. 309(13), 4514–4521, 2519190 (2010j:05134).

http://dx.doi.org/10.1016/j.disc.2009.02.014

598. K. Etessami and M. Yannakakis [2010], On the complexity of Nash equilibria and other fixed points, SIAM J. Comput. 39(6), 2531–2597, 2644357 (2011i:91013).

http://dx.doi.org/10.1137/080720826

599. G. Etienne [1991], Tableaux de Young et solitaire bulgare, J. Combin. Theory (Ser. A) 58, 181–197, MR1129115 (93a:05134).

600. J. M. Ettinger [2000], A metric for positional games, Theoret. Comput. Sci. (Math Games) 230, 207–219, MR1725638 (2001g:91041).

601. M. Euwe [1929], Mengentheoretische Betrachtungen über das Schachspiel, Proc. Konin. Akad. Wetenschappen 32, 633–642.

602. R. J. Evans [1974], A winning opening in reverse Hex, J. Recr. Math. 7, 189–192.

603. R. J. Evans [1975–76], Some variants of Hex, J. Recr. Math. 8, 120–122.

604. R. J. Evans [1979], Silverman’s game on intervals, Amer. Math. Monthly 86, 277–281.

605. R. J. Evans and G. A. Heuer [1992], Silverman’s game on discrete sets, Linear Algebra Appl. 166, 217–235.

606. S. Even and R. E. Tarjan [1976], A combinatorial problem which is complete in polynomial space, J. Assoc. Comput. Mach. 23, 710–719, also appeared in Proc. 7th Ann. ACM Symp. Theory of Computing (Albuquerque, NM, 1975), Assoc. Comput. Mach., New York, NY, 1975, pp. 66–71.

607. L. Euler [1759], Solution d’une question curieuse que ne paroit soumise à aucune analyse, Mmoires de l’Academie Royale des Sciences et Belles Lettres, Berlin 1766 15, 310–337, Publication also listed as Histoire de l’Academie Royale des Sciences et des Belles-Lettres de Berlin, 1759.

608. G. Exoo [1980-81], A new way to play Ramsey games, J. Recr. Math. 13(2), 111–113.

609. U. Faigle, U. Kern, H. Kierstead and W. T. Trotter [1993], On the game chromatic number of some classes of graphs, Ars Combin. 35, 143–150, 1220515 (94b:05079).

610. U. Faigle, W. Kern and J. Kuipers [1998], Computing the nucleolus of min-cost spanning tree games is NP-hard, Internat. J. Game Theory 27, 443–450.

611. E. Falkener [1961], Games Ancient and Oriental and How to Play Them, Dover, New York, NY. (Published previously by Longmans Green, 1892.).

612. B.-J. Falkowski and L. Schmitz [1986], A note on the queens’ problem, Inform. Process. Lett. 23, 39–46.

613. G. E. Farr [2003], The Go polynomials of a graph, Theoret. Comp. Sci. 306, 1–18, MR2000162 (2004e:05074).

614. G. Farr and J. Schmidt [2008], On the number of Go positions on lattice graphs, Inform. Process. Lett. 105(4), 124–130, MR2381402.

http://dx.doi.org/10.1016/j.ipl.2007.08.018

615. J. Farrell, M. Gardner and T. Rodgers [2005], Configuration games, in: Tribute to a Mathemagician, honoring Martin Gardner (B. Cipra, E. D. Demaine, M. L. Demaine and T. Rodgers, eds.), A K Peters, Wellesley, MA, pp. 93-99.

616. T. Feder [1990], Toetjes, Amer. Math. Monthly 97, 785–794.

617. T. Feder and C. Subi [2005], Disks on a tree: analysis of a combinatorial game, SIAM J. Discrete Math. 19, 543–552 (electronic), MR2191279 (2006i:05022).

618. S. P. Fekete, R. Fleischer, A. S. Fraenkel and M. Schmitt [2004], Traveling salesmen in the presence of competition, Theoret. Comp. Sci. 313, 377– 392, special issue of Dagstuhl Seminar “Algorithmic Combinatorial Game Theory”, Feb. 2002, MR2056934 (2005a:90168).

619. A. Ferber and D. Hefetz [2011], Winning strong games through fast strategies for weak games, Electron. J. Combin. 18(1), Paper 144, 13, 2817794.

620. T. S. Ferguson [1974], On sums of graph games with last player losing, Internat. J. Game Theory 3, 159–167.

621. T. S. Ferguson [1984], Misère annihilation games, J. Combin. Theory Ser. A 37(3), 205–230, 769214 (86h:05055).

http://dx.doi.org/10.1016/0097-3165(84)90046-3

622. T. S. Ferguson [1989], Who solved the secretary problem?, Statistical Science 4, 282–296.

623. T. S. Ferguson [1992], Mate with bishop and knight in kriegspiel, Theoret. Comput. Sci. (Math Games) 96, 389–403.

624. T. S. Ferguson [1998], Some chip transfer games, Theoret. Comp. Sci. (Math Games) 191, 157–171.

625. T. S. Ferguson [2001], Another form of matrix Nim, Electr. J. Combin. 8(2), #R9, 9 pp., Volume in honor of Aviezri S. Fraenkel, MR1853260 (2002g:91046).

http://www.combinatorics.org/

626. A. S. Finbow and B. L. Hartnell [1983], A game related to covering by stars, Ars Combinatoria 16-A, 189–198.

627. A. Fink [2012], Lattice games without rational strategies, J. Combin. Theory Ser. A 119(2), 450–459, 2860605.

http://dx.doi.org/10.1016/j.jcta.2011.10.005

628. A. Fink and R. Guy [2007], The number-pad game, College Math. J. 38(4), 260–264, 2340919.

629. A. Fink and R. Guy [2009], Rick’s tricky six puzzle: S_{5} sits specially in S_{6}, Math. Mag. 82, 83–102, 2512593.

http://dx.doi.org/10.4169/193009809X468896

630. M. J. Fischer and R. N. Wright [1993], An application of game-theoretic techniques to cryptography, Advances in Computational Complexity Theory (New Brunswick, NJ, 1990), DIMACS Ser. Discrete Math. Theoret. Comput. Sci., Vol. 13, pp. 99–118.

631. P. C. Fishburn and N. J. A. Sloane [1989], The solution to Berlekamp’s switching game, Discrete Math. 74, 263–290.

632. D. C. Fisher and J. Ryan [1992], Optimal strategies for a generalized “scissors, paper, and stone” game, Amer. Math. Monthly 99, 935–942.

633. D. C. Fisher and J. Ryan [1995], Probabilities within optimal strategies for tournament games, Discrete Appl. Math. 56, 87–91.

634. D. C. Fisher and J. Ryan [1995], Tournament games and positive tournaments, J. Graph Theory 19, 217–236.

635. E. Fisher and N. Sieben [2008], Rectangular polyomino set weak (1, 2)- achievement games, Theoret. Comput. Sci. 409(3), 333–340, MR2473908 (2010a:91036).

http://dx.doi.org/10.1016/j.tcs.2008.05.024

636. S. L. Fitzpatrick and R. J. Nowakowski [2001], Copnumber of graphs with strong isometric dimension two, Ars Combin. 59, 65–73, MR1832198 (2002b:05053).

637. G. W. Flake and E. B. Baum [2002], Rush Hour is PSPACE-complete, or ”Why you should generously tip parking lot attendants”, Theoret. Comput. Sci. (Math Games) 270, 895–911, MR1871102 (2002h:68068).

638. A. Flammenkamp [1996], Lange Perioden in Subtraktions-Spielen, Ph.D. Thesis, University of Bielefeld.

639. A. Flammenkamp, A. Holshouser and H. Reiter [2003], Dynamic one-pile blocking Nim, Electron. J. Combin. 10, Note 4, 6 pp. (electronic), MR1975777 (2004b:05027).

http://www.combinatorics.org/Volume_10/Abstracts/v10i1n4.
html

640. J. A. Flanigan [1978], Generalized two-pile Fibonacci nim, Fibonacci Quart. 16, 459–469.

641. J. A. Flanigan [1981], On the distribution of winning moves in random game trees, Bull. Austr. Math. Soc. 24, 227–237.

642. J. A. Flanigan [1981], Selective sums of loopy partizan graph games, Internat. J. Game Theory 10, 1–10.

643. J. A. Flanigan [1982], A complete analysis of black-white Hackendot, Internat. J. Game Theory 11, 21–25.

644. J. A. Flanigan [1982], One-pile time and size dependent take-away games, Fibonacci Quart. 20, 51–59.

645. J. A. Flanigan [1983], Slow joins of loopy games, J. Combin. Theory Ser. A 34(1), 46–59, 685211 (84b:90106).

http://dx.doi.org/10.1016/0097-3165(83)90039-0

646. R. Fleischer and G. Trippen [2006], Kayles on the way to the stars, Proc. 4th Intern. Conference on Computers and Games CG’2004 (H. J. van den Herik, Y. Björnsson and N. S. Netanyahu, eds.), Bar-Ilan University, Ramat-Gan, Israel, July 2004, Lecture Notes in Computer Science Vol. 3846, Springer, pp. 232–245.

647. R. Fleischer and G. J. Woeginger [2012], An algorithmic analysis of the Honey-Bee game, Theoret. Comput. Sci. 452, 75–87.

648. J. O. Flynn [1973], Lion and man: the boundary constraint, SIAM J. Control 11, 397–411.

649. J. O. Flynn [1974], Lion and man: the general case, SIAM J. Control 12, 581–597.

650. J. O. Flynn [1974], Some results on max-min pursuit, SIAM J. Control 12, 53–69.

651. F. V. Fomin [1998], Helicopter search problems, bandwidth and pathwidth, Discrete Appl. Math. 85, 59–70.

652. F. V. Fomin [1999], Note on a helicopter search problem on graphs, Discrete Appl. Math. 95, 241–249, Proc. Conf. on Optimal Discrete Structures and Algorithms — ODSA ’97 (Rostock).

653. F. V. Fomin and P. A. Golovach [2000], Graph searching and interval completion, SIAM J. Discrete Math. 13(4), 454–464 (electronic), 1787933 (2001e:05123).

http://dx.doi.org/10.1137/S0895480199350477

654. F. V. Fomin, P. A. Golovach and J. Kratochvil [2008], On tractability of cops and robbers game, in: Fifth IFIP International Conference on Theoretical Computer Science—TCS 2008 , Vol. 273 of IFIP Int. Fed. Inf. Process., Springer, New York, pp. 171–185, 2757374 (2012b:91044).

http://dx.doi.org/10.1007/978-0-387-09680-3_12

655. F. V. Fomin, P. A. Golovach, J. Kratochvíl, N. Nisse and K. Suchan [2010], Pursuing a fast robber on a graph, Theoret. Comput. Sci. 411(7-9), 1167–1181, 2606052 (2011f:68055).

http://dx.doi.org/10.1016/j.tcs.2009.12.010

656. F. V. Fomin, P. A. Golovach and D. Lokshtanov [2011], Guard games on graphs: keep the intruder out!, Theoret. Comput. Sci. 412(46), 6484– 6497, 2883020.

http://dx.doi.org/10.1007/978-3-642-12450-1_14

657. F. V. Fomin, P. A. Golovach and N. N. Petrov [1998], Search problems on 1-skeletons of regular polyhedrons, Int. J. Math. Game Theory Algebra 7(2-3), 101–111, 1617256 (99h:90129).

658. F. V. Fomin and N. N. Petrov [1996], Pursuit-evasion and search problems on graphs, Congr. Numer. 122, 47–58, Proc. 27-th Southeastern Intern. Conf. on Combinatorics, Graph Theory and Computing (Baton Rouge, LA, 1996).

659. D. Forge and A. Vieilleribière [2009], The directed switching game on Lawrence oriented matroids, European J. Combin. 30(8), 1833–1834, 2552665 (2011a:05066).

http://dx.doi.org/10.1016/j.ejc.2008.12.002

660. L. R. Foulds and D. G. Johnson [1984], An application of graph theory and integer programming: chessboard non-attacking puzzles, Math. Mag. 57, 95–104.

661. A. S. Fraenkel [1974], Combinatorial games with an annihilation rule, in: The influence of computing on mathematical research and education (Proc. Sympos. Appl. Math., Vol. 20, Univ. Montana, Missoula, Mont., 1973), Amer. Math. Soc., Providence, R.I., pp. 87–91, 0354027 (50 #6509).

662. A. S. Fraenkel [1977], The particles and antiparticles game, Comput. Math. Appl. 3, 327–328.

663. A. S. Fraenkel [1980], From Nim to Go, Ann. Discrete Math. 6, 137–156, Combinatorial mathematics, optimal designs and their applications (Proc. Sympos. Combin. Math. and Optimal Design, Colorado State Univ., Fort Collins, Colo., 1978), 593528 (82e:90117).

664. A. S. Fraenkel [1981], Planar kernel and Grundy with d ≤ 3, d_{out} ≤ 2, d_{in} ≤ 2 are NP-complete, Discrete Appl. Math. 3(4), 257–262, 675689 (83j:68048).

http://dx.doi.org/10.1016/0166-218X(81)90003-2

665. A. S. Fraenkel [1982], How to beat your Wythoff games’ opponent on three fronts, Amer. Math. Monthly 89(6), 353–361, 660914 (84k:90099).

http://dx.doi.org/10.2307/2321643

666. A. S. Fraenkel [1983], 15 Research problems on games, Discrete Math. in ”Research Problems” section, Vols. 43-46.

667. A. S. Fraenkel [1984], Wythoff games, continued fractions, cedar trees and Fibonacci searches, Theoret. Comput. Sci. 29, 49–73, an earlier version appeared in Proc. 10th Internat. Colloq. on Automata, Languages and Programming (J. Diaz, ed.), Vol. 154, Barcelona, July 1983, Lecture Notes in Computer Science, Springer Verlag, Berlin, 1983, pp. 203–225.

668. A. S. Fraenkel [1988], The complexity of chess, Letter to the Editor, J. Recr. Math. 20, 13–14.

669. A. S. Fraenkel [1991], Complexity of games, in: Combinatorial games (Columbus, OH, 1990), Vol. 43 of Proc. Sympos. Appl. Math., Amer. Math. Soc., Providence, RI, pp. 111–153, 1095543.

670. A. Fraenkel [1994], Even kernels, Electron. J. Combin. 1, Research Paper 5, approx. 13 pp. (electronic), 1269166 (95c:05095).

http://www.combinatorics.org/Volume_1/Abstracts/v1i1r5.html

671. A. S. Fraenkel [1994], Iterated floor function, algebraic numbers, discrete chaos, Beatty subsequences, semigroups, Trans. Amer. Math. Soc. 341, 639–664, MR1138949 (94d:11011).

672. A. S. Fraenkel [1994], Recreation and depth in combinatorial games, in: The Lighter Side of Mathematics, Proc. E. Strens Memorial Conf. on Recr. Math. and its History, Calgary, 1986, Spectrum Series (R. K. Guy and R. E. Woodrow, eds.), Math. Assoc. of America, Washington, DC, pp. 176–194.

673. A. S. Fraenkel [1996], Combinatorial games: selected bibliography with a succinct gourmet introduction, in: Games of No Chance (Berkeley, CA, 1994), Vol. 29 of Math. Sci. Res. Inst. Publ., Cambridge Univ. Press, Cambridge, pp. 493–537, 666 bibliographic items; earlier version in Combinatorial Games, AMS 1991 (400 items); later versions: More Games of No Chance (919 items), Games of No Chance 3 (1,360 items). Also in Dynamic Reviews, Electron. J. Combin., 1427984.

674. A. S. Fraenkel [1996], Error-correcting codes derived from combinatorial games, in: Games of no chance (Berkeley, CA, 1994), Vol. 29 of Math. Sci. Res. Inst. Publ., Cambridge Univ. Press, Cambridge, pp. 417–431, 1427980 (98h:94023).

675. A. S. Fraenkel [1996], Scenic trails ascending from sea-level Nim to alpine chess, in: Games of no chance (Berkeley, CA, 1994), Vol. 29 of Math. Sci. Res. Inst. Publ., Cambridge Univ. Press, Cambridge, pp. 13–42, 1427955 (98b:90195).

676. A. S. Fraenkel [1997], Combinatorial game theory foundations applied to digraph kernels, Electron. J. Combin. 4(2), Research Paper 10, approx. 17 pp. (electronic), The Wilf Festschrift (Philadelphia, PA, 1996), 1444157 (98d:05138).

http://www.combinatorics.org/Volume_4/Abstracts/v4i2r10.html

677. A. S. Fraenkel [1998], Heap games, numeration systems and sequences, Ann. Comb. 2, 197–210, an earlier version appeared in: Fun With Algorithms, Vol. 4 of Proceedings in Informatics (E. Lodi, L. Pagli and N. Santoro, eds.), Carleton Scientific, University of Waterloo, Waterloo, Ont., pp. 99–113, 1999. Conference took place on the island of Elba, June 1998., MR1681514 (2000b:91001).

678. A. S. Fraenkel [1998], Multivision: an intractable impartial game with a linear winning strategy, Amer. Math. Monthly 105(10), 923–928, 1656919 (99j:90134).

http://dx.doi.org/10.2307/2589284

679. A. S. Fraenkel [2000], Recent results and questions in combinatorial game complexities, Theoret. Comput. Sci. 249, 265–288, Conference version in: Proc. AWOCA98 — Ninth Australasian Workshop on Combinatorial Algorithms, C.S. Iliopoulos, ed., Perth, Western Australia, 27–30 July, 1998, special AWOCA98 issue, pp. 124-146, MR1798313 (2001j:91033).

680. A. S. Fraenkel [2002], Virus versus mankind, in: Computers and games (Hamamatsu, 2000), Vol. 2063 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 204–213, 1909611.

http://dx.doi.org/10.1007/3-540-45579-5_13

681. A. S. Fraenkel [2002], Arrays, numeration systems and Frankenstein games, Theoret. Comput. Sci. 282, 271–284, special“ Fun With Algorithms” issue, MR1909052 (2003h:91036).

682. A. S. Fraenkel [2002], Mathematical chats between two physicists, in: Puzzler’s Tribute: a Feast for the Mind, honoring Martin Gardner (D. Wolfe and T. Rodgers, eds.), A K Peters, Natick, MA, pp. 383-386.

683. A. S. Fraenkel [2002], Two-player games on cellular automata, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 279–306, MR1973018 (2004b:91004).

684. A. S. Fraenkel [2004], Complexity, appeal and challenges of combinatorial games, Theoret. Comp. Sci. 313, 393–415, Expanded version of a keynote address at Dagstuhl Seminar “Algorithmic Combinatorial Game Theory”, Feb. 2002, special issue on Algorithmic Combinatorial Game Theory, MR2056935.

http://dx.doi.org/10.1016/j.tcs.2002.11.001

685. A. S. Fraenkel [2004], New games related to old and new sequences, Integers 4, G6, 18, 2116012 (2005h:11048).

686. A. S. Fraenkel [2005], Euclid and Wythoff games, Discrete Math. 304, 65–68, MR2184445 (2006f:91006).

687. A. S. Fraenkel [2006], Nim is easy, chess is hard — but why??, J. Internat. Computer Games Assoc. 29(4), 203–206, earlier version appeared in Plus Mag. (electronic), pluschat section, http://plus.maths.org/issue40/editorial/index.html.

688. A. S. Fraenkel [2007], The Raleigh game, in: Combinatorial Number Theory, de Gruyter, pp. 199–208, Proc. Integers Conference, Carrollton, Georgia, October 27-30,2005, in celebration of the 70th birthday of Ronald Graham. B. Landman, M. Nathanson, J. Nešetřil, R. Nowakowski, C. Pomerance eds., also appeared in Integers, Electr. J. of Combinat. Number Theory 7(2), special volume in honor of Ron Graham, #A13, 11 pp., MR2337047 (2008e:91021).

http://www.integers-ejcnt.org/vol7(2).html

689. A. S. Fraenkel [2007], Why are games exciting and stimulating?, Math Horizons pp. 5–7; 32–33, special issue: “Games, Gambling, and Magic” February. German translation by Niek Neuwahl, poster-displayed at traveling exhibition “Games & Science, Science & Games”, opened in Göttingen July 17 – Aug 21, 2005.

690. A. S. Fraenkel [2008], Games played by Boole and Galois, Discrete Appl. Math. 156, 420–427, 2379074 (2009a:91025).

http://dx.doi.org/10.1016/j.dam.2006.06.017

691. A. S. Fraenkel [2009], The cyclic Butler University game, in: Mathematical Wizardry for a Gardner, Volume honoring Martin Gardner, A K Peters, Natick, MA, pp. 97–105, E. Pegg Jr, A. H. Schoen, and T. Rodgers, eds.

692. A. S. Fraenkel [2010], Complementary iterated floor words and the Flora game, SIAM J. Discrete Math. 24(2), 570–588, 2661423 (2011g:91033).

http://dx.doi.org/10.1137/090758994

693. A. S. Fraenkel [2010], From enmity to amity, Amer. Math. Monthly 117(7), 646–648, 2681526.

http://dx.doi.org/10.4169/000298910X496787

694. A. S. Fraenkel [2011], Aperiodic subtraction games, Electron. J. Combin. 18(2), Paper 19, 12, 2830984 (2012g:91039).

695. A. S. Fraenkel [2012], The vile, dopey, evil and odious game players, Discrete Math. 312, 42–46, special volume in honor of the 80th birthday of Gert Sabidussi, 2852506.

http://dx.doi.org/10.1016/j.disc.2011.03.032

696. A. S. Fraenkel [2012], Ratwyt, The College Math. J. In press. In memory of Martin Gardner.

697. A. S. Fraenkel [2013], The Rat Game and the Mouse Game, in: Games of No Chance 4 , Cambridge University Press, to appear.

698. A. S. Fraenkel and I. Borosh [1973], A generalization of Wythoff’s game, J. Combinatorial Theory Ser. A 15, 175–191, 0339824 (49 #4581).

699. A. S. Fraenkel, M. R. Garey, D. S. Johnson, T. Schaefer and Y. Yesha [1978], The complexity of checkers on an n × n board — preliminary report, Proc. 19th Ann. Symp. Foundations of Computer Science (Ann Arbor, MI, Oct. 1978), IEEE Computer Soc., Long Beach, CA, pp. 55–64.

700. A. S. Fraenkel and E. Goldschmidt [1987], PSPACE-hardness of some combinatorial games, J. Combin. Theory Ser. A 46(1), 21–38, 899900 (88j:68049).

http://dx.doi.org/10.1016/0097-3165(87)90074-4

701. A. S. Fraenkel and F. Harary [1989], Geodetic contraction games on graphs, Internat. J. Game Theory 18(3), 327–338, 1024962 (90m:90309).

http://dx.doi.org/10.1007/BF01254296

702. A. S. Fraenkel and H. Herda [1980], Never rush to be first in playing Nimbi, Math. Mag. 53(1), 21–26, 560015 (82f:90101).

http://dx.doi.org/10.2307/2690025

703. A. S. Fraenkel, A. Jaffray, A. Kotzig and G. Sabidussi [1995], Modular Nim, Theoret. Comput. Sci. 143(2), 319–333, 1335685 (96f:90137).

http://dx.doi.org/10.1016/0304-3975(94)00260-P

704. A. S. Fraenkel and C. Kimberling [1994], Generalized Wythoff arrays, shuffles and interspersions, Discrete Math. 126, 137–149, MR1264482 (95c:11028).

705. A. S. Fraenkel and A. Kontorovich [2007], The Sierpiński sieve of Nimvarieties and binomial coefficients, in: Combinatorial Number Theory, de Gruyter, pp. 209–227, Proc. Integers Conference, Carrollton, Georgia, October 27-30,2005, in celebration of the 70th birthday of Ronald Graham. B. Landman, M. Nathanson, J. Nešetřil, R. Nowakowski, C. Pomerance eds., appeared also in Integers, Electr. J. of Combinat. Number Theory 7(2), special volume in honor of Ron Graham, A14, 19 pp., MR2337048.

http://www.integers-ejcnt.org/vol7(2).html

706. A. S. Fraenkel and A. Kotzig [1987], Partizan octal games: partizan subtraction games, Internat. J. Game Theory 16(2), 145–154, 887178 (88c:90145).

http://dx.doi.org/10.1007/BF01780638

707. A. S. Fraenkel and D. Krieger [2004], The structure of complementary sets of integers: a 3-shift theorem, Internat. J. Pure and Appl. Math. 10, 1–49, MR2020683 (2004h:05012).

708. A. S. Fraenkel and D. Lichtenstein [1981], Computing a perfect strategy for n×n chess requires time exponential in n, J. Combin. Theory (Ser. A) 31, 199–214, preliminary version in Proc. 8th Internat. Colloq. Automata, Languages and Programming (S. Even and O. Kariv, eds.), Vol. 115, Acre, Israel, 1981, Lecture Notes in Computer Science, Springer Verlag, Berlin, pp. 278–293, MR629595 (83b:68044).

709. A. S. Fraenkel, M. Loebl and J. Nešetřil [1988], Epidemiography. II. Games with a dozing yet winning player, J. Combin. Theory Ser. A 49(1), 129–144, 957212 (90e:90170).

http://dx.doi.org/10.1016/0097-3165(88)90030-1

710. A. S. Fraenkel and M. Lorberbom [1989], Epidemiography with various growth functions, Discrete Appl. Math. 25(1-2), 53–71, Combinatorics and complexity (Chicago, IL, 1987), 1031263 (90m:90310).

http://dx.doi.org/10.1016/0166-218X(89)90046-2

711. A. S. Fraenkel and M. Lorberbom [1991], Nimhoff games, J. Combin. Theory Ser. A 58(1), 1–25, 1119698 (92i:90136).

http://dx.doi.org/10.1016/0097-3165(91)90070-W

712. A. S. Fraenkel and J. Nešetřil [1985], Epidemiography, Pacific J. Math. 118(2), 369–381, 789177 (87a:90152).

http://projecteuclid.org/getRecord?id=euclid.pjm/1102706445

713. A. S. Fraenkel and M. Ozery [1998], Adjoining to Wythoff’s game its P -positions as moves, Theoret. Comput. Sci. 205(1-2), 283–296, 1638601 (99m:90185).

http://dx.doi.org/10.1016/S0304-3975(98)00044-9

714. A. S. Fraenkel and U. Peled [2013], Harnessing the Unwieldy MEX Function, in: Games of No Chance 4 , Cambridge University Press, to appear.

715. A. S. Fraenkel and Y. Perl [1975], Constructions in combinatorial games with cycles, in: Infinite and finite sets (Colloq., Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vol. II , North-Holland, Amsterdam, pp. 667–699. Colloq. Math. Soc. Janós Bolyai, Vol. 10, 0384171 (52 #5048).

716. A. S. Fraenkel and O. Rahat [2001], Infinite cyclic impartial games, Theoret. Comput. Sci. 252, 13–22, special ”Computers and Games” issue; first version appeared in Proc. 1st Intern. Conf. on Computer Games CG’98, Tsukuba, Japan, Nov. 1998, Lecture Notes in Computer Science, Vol. 1558, Springer, pp. 212-221, 1999., MR1715689 (2000m:91028).

717. A. S. Fraenkel and O. Rahat [2003], Complexity of error-correcting codes derived from combinatorial games, Proc. Intern. Conference on Computers and Games CG’2002, Edmonton, Alberta, Canada, July 2002, (Y. Björnsson, M. Müller and J. Schaeffer, eds.), Vol. LNCS 2883, Lecture Notes in Computer Science, Springer, pp. 201–21.

718. A. S. Fraenkel and E. Reisner [2009], The game of End-Wythoff, in:

Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 329–347.

719. A. S. Fraenkel and E. R. Scheinerman [1991], A deletion game on hypergraphs, Discrete Appl. Math. 30(2-3), 155–162, ARIDAM III (New Brunswick, NJ, 1988), 1095370 (92a:90102).

http://dx.doi.org/10.1016/0166-218X(91)90041-T

720. A. S. Fraenkel, E. R. Scheinerman and D. Ullman [1993], Undirected edge geography, Theoret. Comput. Sci. 112(2), 371–381, 1216328 (94a:90043).

http://dx.doi.org/10.1016/0304-3975(93)90026-P

721. A. S. Fraenkel and S. Simonson [1993], Geography, Theoret. Comput. Sci. 110(1), 197–214, 1208665 (94h:90083).

http://dx.doi.org/10.1016/0304-3975(93)90356-X

722. A. S. Fraenkel and Y. Tanny [2013], A class of Wythoff-like games, in: Combinatorial Number Theory, de Gruyter, Proc. Integers Conference, Carrollton, Georgia, October 26-29, 2011, Integers, Electr. J. of Combinat. Number Theory 12(B) (2013) A7, 18pp.

723. A. S. Fraenkel and U. Tassa [1975], Strategy for a class of games with dynamic ties, Comput. Math. Appl. 1(no.2), 237–254, 0414115 (54 #2220).

724. A. S. Fraenkel and U. Tassa [1982], Strategies for compounds of partizan games, Math. Proc. Cambridge Philos. Soc. 92(2), 193–204, 671176 (84k:90100).

http://dx.doi.org/10.1017/S0305004100059867

725. A. S. Fraenkel, U. Tassa and Y. Yesha [1978], Three annihilation games, Math. Mag. 51(1), 13–17, 0496795 (58 #15272).

726. A. S. Fraenkel and Y. Yesha [1976], Theory of annihilation games, Bull. Amer. Math. Soc. 82(5), 775–777, 0449726 (56 #8027).

727. A. S. Fraenkel and Y. Yesha [1979], Complexity of problems in games, graphs and algebraic equations, Discrete Appl. Math. 1(1-2), 15–30, 544387 (81c:90091).

http://dx.doi.org/10.1016/0166-218X(79)90012-X

728. A. S. Fraenkel and Y. Yesha [1982], Theory of annihilation games – I, J. Combin. Theory Ser. B 33(1), 60–86, 678172 (84c:90097).

http://dx.doi.org/10.1016/0095-8956(82)90058-2

729. A. S. Fraenkel and Y. Yesha [1986], The generalized Sprague-Grundy function and its invariance under certain mappings, J. Combin. Theory Ser. A 43(2), 165–177, 867643 (87m:90179).

http://dx.doi.org/10.1016/0097-3165(86)90058-0

730. A. S. Fraenkel and D. Zusman [2001], A new heap game, Theoret. Comput. Sci. 252, 5–12, special ”Computers and Games” issue; first version appeared in Proc. 1st Intern. Conf. on Computer Games CG’98, Tsukuba, Japan, Nov. 1998, Lecture Notes in Computer Science, Vol. 1558, Springer, pp. 205-211, 1999., MR1715688 (2000m:91027).

731. C. N. Frangakis [1981], A backtracking algorithm to generate all kernels of a directed graph, Intern. J. Comput. Math. 10, 35–41.

732. P. Frankl [1987], Cops and robbers in graphs with large girth and Cayley graphs, Discrete Appl. Math. 17, 301–305.

733. P. Frankl [1987], On a pursuit game on Cayley graphs, Combinatorica 7(1), 67–70, 905152 (88j:90276).

http://dx.doi.org/10.1007/BF02579201

734. P. Frankl and N. Tokushige [2003], The game of n-times nim, Discrete Math. 260, 205–209, MR1948387 (2003m:05017).

735. W. Fraser, S. Hirshberg and D. Wolfe [2005], The structure of the distributive lattice of games born by day n, Integers, Electr. J of Combinat. Number Theory 5(2), #A06, 11 pp., MR2192084 (2006g:91041).

http://www.integers-ejcnt.org/vol5(2).html

736. D. Fremlin [1973], Well-founded games, Eureka 36, 33–37.

737. G. H. Fricke, S. M. Hedetniemi, S. T. Hedetniemi, A. A. McRae, C. K. Wallis, M. S. Jacobson, H. W. Martin and W. D. Weakley [1995], Combinatorial problems on chessboards: a brief survey, in: Graph Theory, Combinatorics, and Algorithms: Proc. 7th Quadrennial Internat. Conf. on the Theory and Applications of Graphs (Y. Alavi and A. Schwenk, eds.), Vol. 1, Wiley, pp. 507–528.

738. E. J. Friedman and A. S. Landsberg [2007], Nonlinear dynamics in combinatorial games: renormalizing Chomp, Chaos 17(2), 023117 1–14, MR2340612.

739. E. J. Friedman and A. S. Landsberg [2009], On the geometry of combinatorial games: a renormalization approach, in: Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 349–376.

740. E. J. Friedman and A. S. Landsberg [2007], Scaling, renormalization, and universality in combinatorial games: the geometry of Chomp, in: Combinatorial optimization and applications, Vol. 4616 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 200–207, 2391862 (2009e:91045).

http://dx.doi.org/10.1007/978-3-540-73556-4_23

741. A. Frieze, M. Krivelevich, O. Pikhurko and T. Szabó [2005], The game of JumbleG, Combin. Probab. Comput. 14, 783–793, MR2174656 (2006k:05207).

742. M. Fukuyama [2003], A Nim game played on graphs, Theoret. Comput. Sci. 304, 387–399, MR1992342 (2004f:91041).

743. M. Fukuyama [2003], A Nim game played on graphs II, Theoret. Comput. Sci. 304, 401–419, MR1992343 (2004g:91036).

744. G. Fülep and N. Sieben [2010], Polyiamonds and polyhexes with minimum site-perimeter and achievement games, Electron. J. Combin. 17(1), Research Paper 65, 14, 2644851 (2011d:05078).

http://www.combinatorics.org/Volume_17/Abstracts/v17i1r65.

html

745. W. W. Funkenbusch [1971], SIM as a game of chance, J. Recr. Math. 4(4), 297–298.

746. Z. Füredi and Á. Seress [1994], Maximal triangle-free graphs with restrictions on the degrees, J. Graph Theory 18, 11–24.

747. H. N. Gabow and H. H. Westermann [1992], Forests, frames, and games: algorithms for matroid sums and applications, Algorithmica 7, 465–497.

748. T. Gagie [2012], Bounds from a card trick, J. Discrete Algorithms 10, 2–4.

749. D. Gale [1974], A curious Nim-type game, Amer. Math. Monthly 81, 876– 879.

750. D. Gale [1979], The game of Hex and the Brouwer fixed-point theorem, Amer. Math. Monthly 86, 818–827.

751. D. Gale [1986], Problem 1237 (line-drawing game), Math. Mag. 59, 111, solution by J. Hutchinson and S. Wagon, ibid. 60 (1987) 116.

752. D. Gale [1991 – 1996], Mathematical Entertainments, Math. Intelligencer 13 - 18, column on mathematical games and gems, Winter 1991 – Fall 1996.

753. D. Gale [1993], The industrious ant, Math. Intelligencer 15, 54–58.

754. D. Gale [1998], Tracking the Automatic Ant and Other Mathematical Explorations, Springer-Verlag, New York, A collection of Mathematical Entertainments columns from The Mathematical Intelligencer.

755. D. Gale and A. Neyman [1982], Nim-type games, Internat. J. Game Theory 11, 17–20.

756. D. Gale, J. Propp, S. Sutherland and S. Troubetzkoy [1995], Further travels with my ant, Math. Intelligencer 17 issue 3, 48–56.

757. D. Gale and F. M. Stewart [1953], Infinite games with perfect information, Ann. of Math. Stud. (Contributions to the Theory of Games), Princeton 2(28), 245–266.

758. H. Galeana-Sánchez [1982], A counterexample to a conjecture of Meyniel on kernel-perfect graphs, Discrete Math. 41, 105–107.

759. H. Galeana-Sánchez [1986], A theorem about a conjecture of Meyniel on kernel-perfect graphs, Discrete Math. 59, 35–41.

760. H. Galeana-Sánchez [1988], A new method to extend kernel-perfect graphs to kernel-perfect critical graphs, Discrete Math. 69, 207–209, MR937787 (89d:05086).

761. H. Galeana-Sánchez [1990], On the existence of (k, l)-kernels in digraphs, Discrete Math. 85, 99–102, MR1078316 (91h:05056).

762. H. Galeana-Sánchez [1992], On the existence of kernels and h-kernels in directed graphs, Discrete Math. 110, 251–255.

763. H. Galeana-Sánchez [1995], B_{1} and B_{2}-orientable graphs in kernel theory, Discrete Math. 143, 269–274.

764. H. Galeana-Sánchez [1996], On claw-free M-oriented critical kernelimperfect digraphs, J. Graph Theory 21, 33–39, MR1363686 (96h:05089).

765. H. Galeana-Sánchez [1998], Kernels in edge-colored digraphs, Discrete Math. 184, 87–99, MR1609359 (99a:05055).

766. H. Galeana-Sánchez [2000], Semikernels modulo F and kernels in digraphs, Discrete Math. 218, 61–71, MR1754327 (2001d:05068).

767. H. Galeana-Sánchez [2002], Kernels in digraphs with covering number at most 3, Discrete Math. 259, 121–135, MR1948776 (2003m:05090).

768. H. Galeana-Sánchez [2004], Some sufficient conditions on odd directed cycles of bounded length for the existence of a kernel, Discuss. Math. Graph Theory 24, 171–182, MR2120561 (2005m:05104).

769. H. Galeana-Sánchez [2006], Kernels and perfectness in arc-local tournament digraphs, Discrete Math. 306(19-20), 2473–2480, special issue: Creation and Recreation: A Tribute to the Memory of Claude Berge, MR2261913 (2007g:05071).

770. H. Galeana-Sánchez [2008], Kernels in edge-coloured orientations of nearly complete graphs, Discrete Math. 308(20), 4599–4607, 2438165 (2009e:05115).

http://dx.doi.org/10.1016/j.disc.2007.08.079

771. H. Galeana-Sánchez [2012], A new characterization of perfect graphs, Discrete Math. 312(17), 2751–2755.

772. H. Galeana-Sánchez and J. de J. García-Ruvalcaba [2000], Kernels in the closure of coloured digraphs, Discuss. Math. Graph Theory 20, 243–254, MR1817495 (2001m:05123).

773. H. Galeana-Sánchez and J. d. J. García-Ruvalcaba [2001], On graphs all of whose {C_{3}, T_{3}}-free arc colorations are kernel-perfect, Discuss. Math. Graph Theory 21(1), 77–93, MR1867488 (2002j:05075).

774. H. Galeana-Sánchez and M.-k. Guevara [2007], Kernel perfect and critical kernel imperfect digraphs structure, in: 6th Czech-Slovak International Symposium on Combinatorics, Graph Theory, Algorithms and Applications, Vol. 28 of Electron. Notes Discrete Math., Elsevier, Amsterdam, pp. 401–408, MR2324045.

775. H. Galeana-Sánchez and M.-k. Guevara [2009], Some sufficient conditions for the existence of kernels in infinite digraphs, Discrete Math. 309, 3680– 3693, 2528045 (2010h:05211).

http://dx.doi.org/10.1016/j.disc.2008.01.025

776. H. Galeana-Sánchez and X. Li [1998], Kernels in a special class of digraphs, Discrete Math. 178, 73–80, MR1483740 (98f:05073).

777. H. Galeana-Sánchez and X. Li [1998], Semikernels and (k, l)-kernels in digraphs, SIAM J. Discrete Math. 11, 340–346 (electronic), MR1617163 (99c:05078).

778. H. Galeana-Sánchez and V. Neumann-Lara [1984], On kernels and semikernels of digraphs, Discrete Math. 48, 67–76.

779. H. Galeana-Sánchez and V. Neumann Lara [1986], On kernel-perfect critical digraphs, Discrete Math. 59, 257–265, MR842278 (88b:05069).

780. H. Galeana-Sánchez and V. Neumann-Lara [1991], Extending kernel perfect digraphs to kernel perfect critical digraphs, Discrete Math. 94, 181– 187.

781. H. Galeana-Sánchez and V. Neumann Lara [1991], Orientations of graphs in kernel theory, Discrete Math. 87, 271–280, MR1095472 (92d:05134).

782. H. Galeana-Sánchez and V. Neumann-Lara [1994], New extensions of kernel perfect digraphs to kernel imperfect critical digraphs, Graphs Combin. 10, 329–336.

783. H. Galeana-Sánchez and V. Neumann-Lara [1998], New classes of critical kernel-imperfect digraphs, Discuss. Math. Graph Theory 18, 85–89, MR1646233 (99g:05087).

784. H. Galeana-Sánchez and V. Neumann-Lara [1998], On the dichromatic number in kernel theory, Math. Slovaca 48, 213–219, MR1647678 (99k:05080).

785. H. Galeana-Sánchez and M. Olsen [2011], Kernels by monochromatic paths in digraphs with covering number 2, Discrete Math. 311(13), 1111– 1118, 2793221 (2012d:05166).

http://dx.doi.org/10.1016/j.disc.2010.09.022

786. H. Galeana-Sánchez and L. Pastrana Ramírez [1998], Kernels in edge coloured line digraph, Discuss. Math. Graph Theory 18, 91–98, MR1646234 (99g:05088).

787. H. Galeana-Sánchez, L. Pastrana Ramírez and H. A. Rincón-Mejía [1991], Semikernels, quasi kernels, and Grundy functions in the line digraph, SIAM J. Discrete Math. 4, 80–83, MR1090291 (92c:05068).

788. H. Galeana-Sánchez, L. P. Ramírez and H. A. Rincón Mejía [2005], Kernels in monochromatic path digraphs, Discuss. Math. Graph Theory 25, 407–417, MR2233005.

789. H. Galeana-Sánchez and H. A. Rincón-Mejía [1998], A sufficient condition for the existence of k-kernels in digraphs, Discuss. Math. Graph Theory 18, 197–204, MR1687843 (2000c:05074).

790. H. Galeana-Sánchez and R. Rojas-Monroy [2004], Kernels in pretransitive digraphs, Discrete Math. 275, 129–136, MR2026280 (2004j:05059).

791. H. Galeana-Sánchez and R. Rojas-Monroy [2006], Kernels in quasitransitive digraphs, Discrete Math. 306(16), 1969–1974, MR2251578 (2007b:05092).

792. H. Galeana-Sánchez and R. Rojas-Monroy [2007], Extensions and kernels in digraphs and in edge-coloured digraphs, WSEAS Trans. Math. 6(2), 334–341, MR2273872.

793. H. Galeana-Sánchez and R. Rojas-Monroy [2007], Kernels in orientations of pretransitive orientable graphs, in: Graph theory in Paris, Trends Math., Birkhäuser, Basel, pp. 197–208, MR2279176.

794. H. Galeana-Sánchez and R. Rojas-Monroy [2008], Kernels and some operations in edge-coloured digraphs, Discrete Math. 308(24), 6036–6046, 2464895 (2009j:05077).

http://dx.doi.org/10.1016/j.disc.2007.11.022

795. R. P. Gallant, G. Gunther, B. L. Hartnell and D. F. Rall [2006], A game of edge removal on graphs, J. Combin. Math. Combin. Comput. 57, 75–82, MR2226684 (2006m:05245).

796. F. Galvin [1978], Indeterminacy of point-open games, Bull. de l’Academie Polonaise des Sciences (Math. astr. et phys.) 26, 445–449.

797. F. Galvin [1985], Stationary strategies in topological games, Proc. Conf. on Infinitistic Mathematics (Lyon, 1984), Publ. Dép. Math. Nouvelle Sér. B, 85–2, Univ. Claude-Bernard, Lyon, pp. 41–43.

798. F. Galvin [1990], Hypergraph games and the chromatic number, in: A Tribute to Paul Erdős, Cambridge Univ Press, Cambridge, pp. 201–206.

799. F. Galvin, T. Jech and M. Magidor [1978], An ideal game, J. Symbolic Logic 43, 284–292.

800. F. Galvin and M. Scheepers [1992], A Ramseyan theorem and an infinite game, J. Combin. Theory Ser. A 59(1), 125–129, 1141327 (93b:90129).

http://dx.doi.org/10.1016/0097-3165(92)90103-2

801. F. Galvin and R. Telgársky [1986], Stationary strategies in topological games, Topology Appl. 22, 51–69.

802. B. B. Gan and Y. N. Yeh [1995], A nim-like game and dynamic recurrence relations, Stud. Appl. Math. 95, 213–228.

803. A. Gangolli and T. Plambeck [1989], A note on periodicity in some octal games, Internat. J. Game Theory 18(3), 311–320, 1024960 (91a:90183).

http://dx.doi.org/10.1007/BF01254294

804. T. E. Gantner [1988], The game of Quatrainment, Math. Mag. 61, 29–34.

805. S. Ganzell and A. Meadows [2009], Untangle: knots in combinatorial game theory, Geombinatorics 18(3), 101–108, 2479639.

806. M. Gardner [1956], Mathematics, Magic and Mystery, Dover, New York, NY.

807. M. Gardner [Jan. 1957–Dec. 1981], Mathematical Games, a column in Scientific American; all 15 volumes of the column are on 1 CD-ROM, available from MAA.

808. M. Gardner [1959], Fads and Fallacies in the Name of Science, Dover, NY.

809. M. Gardner [1959], Logic Machines and Diagrams, McGraw-Hill, NY.

810. M. Gardner [1959], Mathematical Puzzles of Sam Loyd, Dover, New York, NY.

811. M. Gardner [1960], More Mathematical Puzzles of Sam Loyd, Dover, New York, NY.

812. M. Gardner [1966], More Mathematical Puzzles and Diversions, Harmondsworth, Middlesex, England (Penguin Books), translated into German: Mathematische Rätsel und Probleme, Vieweg, Braunschweig, 1964.

813. M. Gardner, ed. [1967], 536 Puzzles and Curious Problems, Scribner’s, NY, reissue of H. E. Dudeney’s Modern Puzzles and Puzzles and Curious Problems.

814. M. Gardner [1968], Logic Machines, Diagrams and Boolean Algebra, Dover, NY.

815. M. Gardner [1970], Further Mathematical Diversions, Allen and Unwin, London.

816. M. Gardner [1977], Mathematical Magic Show, Knopf, NY.

817. M. Gardner [1978], Aha! Insight, Freeman, New York, NY.

818. M. Gardner [1979], Mathematical Circus, Knopf, NY.

819. M. Gardner [1981], Entertaining Science Experiments with Everyday Objects, Dover, NY.

820. M. Gardner [1981], Science Fiction Puzzle Tales, Potter.

821. M. Gardner [1982], Aha! Gotcha!, Freeman, New York, NY.

822. M. Gardner [1983], New Mathematical Diversions from Scientific American, University of Chicago Press, Chicago, before that appeared in 1971, Simon and Schuster, New York, NY. First appeared in 1966.

823. M. Gardner [1983], Order and Surprise, Prometheus Books, Buffalo, NY.

824. M. Gardner [1983], Wheels, Life and Other Mathematical Amusements, Freeman, New York, NY.

825. M. Gardner [1984], Codes, Ciphers and Secret Writing, Dover, NY.

826. M. Gardner [1984], Puzzles from Other Worlds, Random House.

827. M. Gardner [1984], The Magic Numbers of Dr. Matrix, Prometheus.

828. M. Gardner [1984], The Sixth Book of Mathematical Games, Univ. of Chicago Press. First appeared in 1971, Freeman, New York, NY.

829. M. Gardner [1986], Knotted Doughnuts and Other Mathematical Entertainments, Freeman, New York, NY.

830. M. Gardner [1987], The Second Scientific American Book of Mathematical Puzzles and Diversions, University of Chicago Press, Chicago. First appeared in 1961, Simon and Schuster, NY.

831. M. Gardner [1988], Hexaflexagons and Other Mathematical Diversions, University of Chicago Press, Chicago, 1988. A first version appeared under the title The Scientific American Book of Mathematical Puzzles and Diversions, Simon & Schuster, 1959, NY.

832. M. Gardner [1988], Perplexing Puzzles and Tantalizing Teasers, Dover, NY.

833. M. Gardner [1988], Riddles of the Sphinx, Math. Assoc. of America, Washington, DC.

834. M. Gardner [1988], Time Travel and Other Mathematical Bewilderments, Freeman, New York, NY.

835. M. Gardner [1989], How Not to Test a Psychic, Prometheus Books, Buffalo, NY.

836. M. Gardner [1989], Mathematical Carnival, 2nd edition, Math. Assoc. of America, Washington, DC. First appeared in 1975, Knopf, NY.

837. M. Gardner [1990], The New Ambidextrous Universe, Freeman, New York, NY. First appeared in 1964, Basic Books, then in 1969, New American Library.

838. M. Gardner [1991], The Unexpected Hanging and Other Mathematical Diversions, University of Chicago Press. First appeared in 1969, Simon and Schuster, NY, adapted from “Further Mathematical Diversions”; translated into German: Logik Unterm Galgen, Vieweg, Braunschweig, 1980.

839. M. Gardner [1992], Fractal Music, Hypercards and More, Freeman, New York, NY.

840. M. Gardner [1992], On the Wild Side, Prometheus Books, Buffalo, NY.

841. M. Gardner [1993], Book of Visual Illusions, Dover, NY.

842. M. Gardner [1997], Penrose Tiles to Trapdoor Ciphers, The Math. Assoc. of America, Washington, DC. First appeared in 1989, Freeman, New York, NY. Freeman, New York, NY.

843. M. Gardner [1997], The Last Recreations, Copernicus, NY.

844. M. Gardner [2001], A Gardner’s Workout: Training the Mind and Entertaining the Spirit, A K Peters, Natick, MA.

845. M. R. Garey and D. S. Johnson [1979], Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, Appendix A8: Games and Puzzles, pp. 254-258.

846. Q. R. Gashi, T. Schedler and D. E. Speyer [2012], Looping of the numbers game and the alcoved hypercube, J. Combin. Theory Ser. A 119(3), 713– 730, 2871758.

http://dx.doi.org/10.1016/j.jcta.2011.11.012

847. R. Gasser [1996], Solving nine men’s Morris, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 101–114.

848. H. Gavel and P. Strimling [2004], Nim with a modular Muller twist, Integers, Electr. J of Combinat. Number Theory 4, #G4, 9 pp., Comb. Games Sect., MR2116010.

http://www.integers-ejcnt.org/vol4.html

849. T. Gavenčiak [2010], Cop-win graphs with maximum capture-time, Discrete Math. 310(10-11), 1557–1563, 2601265 (2011d:05241).

http://dx.doi.org/10.1016/j.disc.2010.01.015

850. H. Gebauer [2012], On the clique-game, European J. Combin. 33(1), 8– 19, 2854626.

http://dx.doi.org/10.1016/j.ejc.2011.07.005

851. A. Georgakopoulos and P. Winkler [2012], Two-color Babylon, Integers, Electr. J of Combinat. Number Theory 12, #G1, 7 pp., Comb. Games Sect.

http://www.integers-ejcnt.org/vol12.html

852. B. Gerla [2000], Conditioning a state by Łukasiewicz event: a probabilistic approach to Ulam Games, Theoret. Comput. Sci. (Math Games) 230, 149–166, MR1725635 (2001e:03117).

853. C. Germain and H. Kheddouci [2003], Grundy coloring for power graphs, in: Electron. Notes Discrete Math. (D. Ray-Chaudhuri, A. Rao and

B. Roy, eds.), Vol. 15, Elsevier, Amsterdam, pp. 67–69.

854. S. V. Gervacio [1979], On graphs all of whose orientations have kernels, Proceedings of the First Franco-Southeast Asian Mathematical Conference (Singapore, 1979), Vol. II , Vol. 46, pp. 259–263 (1980), MR582263 (83c:05103).

855. N. M. Gibbins [1944], Chess in 3 and 4 dimensions, Math. Gaz. pp. 46–50.

856. P. B. Gibbons and J. A. Webb [1997], Some new results for the queens domination problem, Australas. J. Combin. 15, 145–160.

857. J. R. Gilbert, T. Lengauer and R. E. Tarjan [1980], The pebbling problem is complete in polynomial space, SIAM J. Comput. 9, 513–524, preliminary version in Proc. 11th Ann. ACM Symp. Theory of Computing (Atlanta, GA, 1979), Assoc. Comput. Mach., New York, NY, pp. 237–248.

858. M. Ginsberg [2002], Alpha-beta pruning under partial orders, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 37–48.

859. J. Ginsburg [1939], Gauss’s arithmetization of the problem of 8 queens, Scripta Math. 5, 63–66.

860. M. Goadrich and M. Schlatter [2011], Analyzing two-color Babylon, Integers 11, G01, 12, 2798614 (2012c:91060).

http://dx.doi.org/10.1515/INTEG.2011.001

861. W. Goddard, A. Sinko, P. Slater and H. Xu [2011], The graph distance game, AKCE Int. J. Graphs Comb. 8(1), 85–96, 2839178 (2012e:05252).

862. P. W. Goldberg and C. H. Papadimitriou [2006], Reducibility among equilibrium problems, in: STOC’06: Proceedings of the 38th Annual ACM Symposium on Theory of Computing, ACM, New York, pp. 61– 70, 2277131 (2007h:68083).

http://dx.doi.org/10.1145/1132516.1132526

863. A. S. Goldstein and E. M. Reingold [1995], The complexity of pursuit on a graph, Theoret. Comput. Sci. (Math Games) 143, 93–112.

864. J. Goldwasser and W. Klostermeyer [1997], Maximization versions of “lights out” games in grids and graphs, Congr. Numer. 126, 99–111, Proc. 28th Southeastern Internat. Conf. on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1997), MR1604979 (98j:05119).

865. J. Goldwasser, W. Klostermeyer and G. Trapp [1997], Characterizing switch-setting problems, Linear and Multilinear Algebra 43(1-3), 121– 135, 1613183 (98k:15005).

http://dx.doi.org/10.1080/03081089708818520

866. J. Goldwasser, X. Wang and Y. Wu [2009], Does the lit-only restriction make any difference for the σ-game and σ^{+}-game?, European J. Combin. 30, 774–787, 2504636 (2010c:05087).

http://dx.doi.org/10.1016/j.ejc.2008.09.020

867. J. Goldwasser, X. Wang and Y. Wu [2011], Minimum light numbers in the σ-game and lit-only σ-game on unicyclic and grid graphs, Electron.

J. Combin. 18(1), Paper 214, 27, 2853071.

868. E. Goles [1991], Sand piles, combinatorial games and cellular automata, in: Instabilities and nonequilibrium structures, III (Valparaíso, 1989), Vol. 64 of Math. Appl., Kluwer Acad. Publ., Dordrecht, pp. 101–121, 1177845 (93j:58069).

869. E. Goles and M. A. Kiwi [1993], Games on line graphs and sand piles, Theoret. Comput. Sci. (Math Games) 115, 321–349 (0–player game).

870. E. Goles, M. Latapy, C. Magnien, M. Morvan and H. D. Phan [2004], Sandpile models and lattices: a comprehensive survey, Theoret. Comput. Sci. 322, 383–407, MR2080235 (2005h:05013).

871. E. Goles and M. Margenstern [1997], Universality of the chip-firing game, Theoret. Comput. Sci. (Math Games) 172, 121–134.

872. E. Goles, M. Morvan and H. D. Phan [2002], The structure of a linear chip firing game and related models, Theoret. Comput. Sci. 270, 827–841, MR1871097 (2002k:05013).

873. E. Goles and E. Prisner [2000], Source reversal and chip firing on graphs, Theoret. Comput. Sci. 233, 287–295.

874. S. W. Golomb [1966], A mathematical investigation of games of “takeaway”, J. Combinatorial Theory 1, 443–458, 0209015 (34 #8823).

875. S. W. Golomb [1994], Polyominoes: Puzzles, Patterns, Problems, and Packings, Princeton University Press. Original edition: Polyominoes, Scribner’s, NY, 1965; Allen and Unwin, London, 1965.

876. S. W. Golomb and A. W. Hales [2002], Hypercube Tic-Tac-Toe, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 167–182, MR1973012 (2004c:91030).

877. P. A. Golovach and F. V. Fomin [2001], The search and the node-search number of dual graphs, Vestn. Syktyvkar. Univ. Ser. 1 Mat. Mekh. Inform. (4), 125–136, 1875659 (2002k:05222).

878. H. Gonshor [1986], An Introduction to the Theory of Surreal Numbers, Cambridge University Press, Cambridge.

879. P. Gordinowicz, R. Nowakowski and P. Prałat [2012], POLISH – Let us play the cleaning game, Theoret. Comput. Sci. 463, 123–132.

880. D. M. Gordon, R. W. Robinson and F. Harary [1994], Minimum degree games for graphs, Discrete Math. 128, 151–163, MR1271861 (95b:05201).

881. E. Grädel [1990], Domino games and complexity, SIAM J. Comput. 19, 787–804.

882. S. B. Grantham [1985], Galvin’s “racing pawns” game and a well-ordering of trees, Mem. Amer. Math. Soc. 53(316), iv+63, MR776346 (86d:04002).

883. S. Gravier, P. Jorrand, M. Mhalla and C. Payan [2006], Quantum octal games, Internat. J. Found. Comput. Sci. 17(4), 919–931, 2234074 (2008c:91039).

http://dx.doi.org/10.1142/S0129054106004182

884. S. Gravier, M. Mhalla and E. Tannier [2003], On a modular domination game, Theoret. Comput. Sci. 306, 291–303, MR2000178 (2004i:91041).

885. R. Greenlaw, H. J. Hoover and W. L. Ruzzo [1995], Limits to Parallel Computation: P -completeness Theory, Oxford University Press, New York.

886. D. Griffeath and C. Moore [1996], Life without death is P-complete, Complex Systems 10, 437–447, 1634401 (99d:68168).

887. J. P. Grossman [2004], Periodicity in one-dimensional peg duotaire, Theoret. Comp. Sci. 313, 417–425, special issue of Dagstuhl Seminar “Algorithmic Combinatorial Game Theory”, Feb. 2002, MR2056936 (2005b:91055).

888. J. P. Grossman and R. J. Nowakowski [2002], One-dimensional Phutball, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 361–367, MR1973024.

889. J. P. Grossman and A. N. Siegel [2009], Reductions of partizan games, in: Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 427–445.

890. J. W. Grossman [2000], A variant of Nim, Math. Mag. 73, 323–324, Problem No. 1580; originally posed ibid. 72 (1999) 325.

891. P. M. Grundy [1964], Mathematics and Games, Eureka 27, 9–11, originally published: ibid. 2 (1939) 6–8.

892. P. M. Grundy and C. A. B. Smith [1956], Disjunctive games with the last player losing, Proc. Camb. Phil. Soc. 52, 527–533.

893. F. Grunfeld and R. C. Bell [1975], Games of the World, Holt, Rinehart and Winston.

894. C. D. Grupp [1976], Brettspiele-Denkspiele, Humboldt-Taschenbuchver-lag, München.

895. D. J. Guan and X. Zhu [1999], Game chromatic number of outerplanar graphs, J. Graph Theory 30, 67–70.

896. L. J. Guibas, J.-C. Latombe, S. M. Lavalle, D. Lin and R. Motwani [1999], A visibility-based pursuit-evasion problem, Internat. J. Comput. Geom. Appl. 9, 471–493, MR1712332 (2000e:68177).

897. L. J. Guibas and A. M. Odlyzko [1981], String overlaps, pattern matching, and nontransitive games, J. Combin. Theory (Ser. A) 30, 183–208.

898. A. Guignard and É. Sopena [2009], Compound Node-Kayles on paths, Theoret. Comput. Sci. 410, 2033–2044, 2519292 (2010g:91030).

http://dx.doi.org/10.1016/j.tcs.2008.12.053

899. S. Gunther [1874], Zur mathematischen Theorie des Schachbretts, Arch. Math. Physik 56, 281–292.

900. A. Guo [2012], Winning strategies for aperiodic subtraction games, Theoret. Comput. Sci. 421, 70–73.

901. A. Guo and E. Miller [2011], Lattice point methods for combinatorial games, Adv. in Appl. Math. 46(1-4), 363–378, 2794028.

http://dx.doi.org/10.1016/j.aam.2010.10.004

902. A. Guo and E. Miller [2012], Corrigendum to “Lattice point methods for combinatorial games” [Adv. in Appl. Math. 46 (1–4) (2011) 363–378] [MR2794028], Adv. in Appl. Math. 48(1), 269–271, 2845518.

http://dx.doi.org/10.1016/j.aam.2011.09.001

903. W. Guo, S. Kasala, M. B. Rao and B. Tucker [2006], The hat problem and some variations, in: Advances in distribution theory, order statistics, and inference, Stat. Ind. Technol., Birkhäuser Boston, Boston, MA, pp. 459–479, MR2226238 (2007e:68043).

http://dx.doi.org/10.1007/0-8176-4487-3_29

904. V. A. Gurvich [2007], On the misère version of game Euclid and miserable games, Discrete Math. 307(9-10), 1199–1204, MR2292548 (2007k:91052).

905. V. Gurvich [2012], Further generalizations of the Wythoff game and the minimum excludant, Discrete Appl. Math. 160, 941–947.

906. G. Gutin, K. M. Koh, E. G. Tay and A. Yeo [2004], On the number of quasi-kernels in digraphs, J. Graph Theory 46(1), 48–56, 2051468 (2005e:05067).

http://dx.doi.org/10.1002/jgt.10169

907. G. Gutowski [2011], Mr. Paint and Mrs. Correct go fractional, Electron. J. Combin. 18(1), Paper 140, 8, 2817790.

908. R. K. Guy [1976], Packing [1, n] with solutions of ax + by = cz; the unity of combinatorics, Atti Conv. Lincei #17, Acad. Naz. Lincei, Tomo II , Rome, pp. 173–179.

909. R. K. Guy [1976], Twenty questions concerning Conway’s sylver coinage, Amer. Math. Monthly 83, 634–637.

910. R. K. Guy [1977], Games are graphs, indeed they are trees, Proc. 2nd Carib. Conf. Combin. and Comput., Letchworth Press, Barbados, pp. 6– 18.

911. R. K. Guy [1977], She loves me, she loves me not; relatives of two games of Lenstra, Een Pak met een Korte Broek (papers presented to H. W. Lenstra), Mathematisch Centrum, Amsterdam.

912. R. K. Guy [1978], Partisan and impartial combinatorial games, in: Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely, 1976), Vol. I , Vol. 18 of Colloq. Math. Soc. János Bolyai, North-Holland, Amsterdam, pp. 437– 461, 519283 (80c:90156).

913. R. K. Guy [1979], Partizan Games, Colloques Internationaux C. N. R. No. 260 — Problèmes Combinatoires et Théorie des Graphes, pp. 199–205.

914. R. K. Guy [1981], Anyone for twopins?, in: The Mathematical Gardner (D. A. Klarner, ed.), Wadsworth Internat., Belmont, CA, pp. 2–15.

915. R. K. Guy [1983], Graphs and games, in: Selected topics in graph theory,

2 , Academic Press, London, pp. 269–295, 797255 (87h:90272).

916. R. K. Guy [1986], John Isbell’s game of beanstalk and John Conway’s game of beans-don’t-talk, Math. Mag. 59(5), 259–269, 868803 (88c:90163).

http://dx.doi.org/10.2307/2689400

917. R. K. Guy [1989], Fair Game, COMAP Math. Exploration Series, Arlington, MA.

918. R. K. Guy [1990], A guessing game of Bill Sands, and Bernardo Recamán’s Barranca, Amer. Math. Monthly 97, 314–315.

919. R. K. Guy [1991], Mathematics from fun & fun from mathematics: an informal autobiographical history of combinatorial games, in: Paul Halmos: Celebrating 50 Years of Mathematics (J. H. Ewing and F. W. Gehring, eds.), Springer, New York, pp. 287–295, 1113280.

920. R. K. Guy [1995], Combinatorial games, in: Handbook of combinatorics, Vol. 1, 2 , Elsevier, Amsterdam, pp. 2117–2162, 1373699 (97j:90099).

921. R. K. Guy [1996], Impartial Games, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 61–78, earlier version in: Combinatorial Games, Proc. Symp. Appl. Math. (R. K. Guy, ed.), Vol. 43, Amer. Math. Soc., Providence, RI, 1991, pp. 35–55.

922. R. K. Guy [1996], What is a game?, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 43–60, earlier version in: Combinatorial Games, Proc. Symp. Appl. Math. (R. K. Guy, ed.), Vol. 43, Amer. Math. Soc., Providence, RI, 1991, pp. 1–21.

923. R. K. Guy [1996], Unsolved problems in combinatorial games, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 475–491, update with 52 problems of earlier version with 37 problems, in: Combinatorial Games, Proc. Symp. Appl. Math. (R. K. Guy, ed.), Vol. 43, Amer. Math. Soc., Providence, RI, 1991, pp. 183–189; another version in: Combinatorics Advances (Tehran, 1994), Dordrecht, 1995, 90D46 (05-02).

924. R. K. Guy [2001], Aviezri Fraenkel and combinatorial games, Electron. J. Combin. 8(2), Introduction 2, 6 pp. (electronic), In honor of Aviezri Fraenkel on the occasion of his 70th birthday, 1853249 (2002g:01016).

925. R. K. Guy [2007], A parity subtraction game, Crux Math. 33, 37–39.

926. R. K. Guy and R. J. Nowakowski [1993], Mousetrap, in: Combinatorics, Paul Erdős is eighty, Vol. 1 , Bolyai Soc. Math. Stud., János Bolyai Math. Soc., Budapest, pp. 193–206, 1249712 (94k:05011).

927. R. K. Guy and R. J. Nowakowski [2002], Unsolved problems in combinatorial games, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J.

Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 457–473, also in Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ., pp.465-489, 2009.

928. R. K. Guy, R. J. Nowakowski, I. Caines and C. Gates [1999], Unsolved Problems: periods in taking and splitting games, Amer. Math. Monthly 106, 359–361, Unsolved Problems Section.

929. R. K. Guy and C. A. B. Smith [1956], The G-values of various games, Proc. Cambridge Philos. Soc. 52, 514–526, 0082408 (18,546a).

930. R. K. Guy and R. E. Woodrow, eds. [1994], The Lighter Side of Mathematics, Proc. E. Strens Memorial Conf. on Recr. Math. and its History, Calgary, 1986, Spectrum Series, Math. Assoc. Amer., Washington, DC.

931. W. Guzicki [1990], Ulam’s searching game with two lies, J. Combin. Theory Ser. A 54(1), 1–19, 1051775 (91f:68027).

http://dx.doi.org/10.1016/0097-3165(90)90002-E

932. G. Hahn [2007], Cops, robbers and graphs, Tatra Mt. Math. Publ. 36, 163–176, 2378748 (2009b:05254).

933. G. Hahn, F. Laviolette, N. Sauer and R. E. Woodrow [2002], On cop-win graphs, Discrete Math. 258, 27–41, MR2002070 (2004f:05156).

934. G. Hahn and G. MacGillivray [2006], A note on k-cop, l-robber games on graphs, Discrete Math. 306(19-20), 2492–2497, MR2261915 (2007d:05069).

935. A. Hajnal and Z. Nagy [1984], Ramsey games, Trans. American Math. Soc. 284, 815–827.

936. D. R. Hale [1983], A variant of Nim and a function defined by Fibonacci representation, Fibonacci Quart. 21, 139–142.

937. A. W. Hales and R. I. Jewett [1963], Regularity and positional games, Trans. Amer. Math. Soc. 106, 222–229.

938. L. Halpenny and C. Smyth [1992], A classification of minimal standardpath 2×2 switching networks, Theoret. Comput. Sci. (Math Games) 102, 329–354.

939. I. Halupczok and J.-C. Schlage-Puchta [2007], Achieving snaky, Integers, Electr. J. of Combinat. Number Theory 7, #G02, 28 pp., MR2282185 (2007i:05045).

http://www.integers-ejcnt.org/vol7.html

940. I. Halupczok and J.-C. Schlage-Puchta [2008], Some strategies for higher dimensional animal achievement games, Discrete Math. 308(16), 3470– 3478, 2421669 (2009g:91040).

http://dx.doi.org/10.1016/j.disc.2007.07.005

941. Y. O. Hamidoune [1987], On a pursuit game on Cayley digraphs, European J. Combin. 8(3), 289–295, 919881 (89d:90264).

942. Y. O. Hamidoune and M. Las Vergnas [1985], The directed Shannon switching game and the one-way game, in: Graph Theory with Applications to Algorithms and Computer Science (Y. Alavi et al., eds.), Wiley,

pp. 391–400.

943. Y. O. Hamidoune and M. Las Vergnas [1986], Directed switching games on graphs and matroids, J. Combin. Theory Ser. B 40(3), 237–269, 842994 (87j:90172).

http://dx.doi.org/10.1016/0095-8956(86)90083-3

944. Y. O. Hamidoune and M. Las Vergnas [1987], A solution to the box game, Discrete Math. 65, 157–171.

945. Y. O. Hamidoune and M. Las Vergnas [1988], A solution to the misère Shannon switching game, Discrete Math. 72, 163–166.

946. O. Hanner [1959], Mean play of sums of positional games, Pacific J. Math. 9, 81–99.

947. F. Harary [1982], Achievement and avoidance games for graphs, Ann. Discrete Math. 13, 111–119.

948. F. Harary [2002], Sum-free games, in: Puzzler’s Tribute: a Feast for the Mind, pp. 395–398, honoring Martin Gardner (D. Wolfe and T. Rodgers, eds.), A K Peters, Natick, MA.

949. F. Harary, H. Harborth and M. Seemann [2000], Handicap achievement for polyominoes, Congr. Numer. 145, 65–80, Proc. 31st Southeastern Internat. Conf. on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1999), MR1817942 (2001m:05083).

950. F. Harary and K. Plochinski [1987], On degree achievement and avoidance games for graphs, Math. Mag. 60, 316–321.

951. F. Harary, B. Sagan and D. West [1985], Computer-aided analysis of monotonic sequence games, Atti Accad. Peloritana Pericolanti Cl. Sci. Fis. Mat. Natur. 61, 67–78.

952. F. Harary, W. Slany and O. Verbitsky [2002], A symmetric strategy in graph avoidance games, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 369–381, MR1973105 (2004b:91036).

953. F. Harary, W. Slany and O. Verbitsky [2004], On the length of symmetry breaking-preserving games on graphs, Theoret. Comp. Sci. 313, 427–446, special issue of Dagstuhl Seminar “Algorithmic Combinatorial Game Theory”, Feb. 2002, MR2056937 (2005a:91025).

954. F. Harary and Z. Tuza [1993], Two graph-colouring games, Bull. Austral. Math. Soc. 48(1), 141–149, 1227444 (94d:90084).

http://dx.doi.org/10.1017/S0004972700015549

955. H. Harborth and M. Seemann [1996], Snaky is an edge-to-edge loser, Geombinatorics 5, 132–136, MR1380142.

956. H. Harborth and M. Seemann [1997], Snaky is a paving winner, Bull. Inst. Combin. Appl. 19, 71–78, MR1427578 (97g:05052).

957. H. Harborth and M. Seemann [2003], Handicap achievement for squares, J. Combin. Math. Combin. Comput. 46, 47–52, 15th MCCCC (Las Vegas, NV, 2001), MR2004838 (2004g:05044).

958. F. Havet and L. Sampaio [2010], On the Grundy number of a graph, in: Parameterized and exact computation, Vol. 6478 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 170–179, 2770795 (2012e:05134).

http://dx.doi.org/10.1007/978-3-642-17493-3_17

959. P. J. Hayes [1977], A note on the towers of Hanoi problem, Computer J. 20, 282–285.

960. R. B. Hayward [2009], A puzzling Hex primer, in: Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 151–161.

961. R. Hayward, Y. Björnsson, M. Johanson, M. Kan, N. Po and J. van Rijswijck [2005], Solving 7 × 7 Hex with domination, fill-in, and virtual connections, Theoret. Comput. Sci. 349(2), 123–139, MR2184213 (2006f:68112).

962. R. B. Hayward, B. Toft and P. Henderson [2012], How to play Reverse Hex, Discrete Math. 312(1), 148–156, 2852517.

http://dx.doi.org/10.1016/j.disc.2011.06.033

963. R. B. Hayward and J. van Rijswijck [2006], Hex and combinatorics, Discrete Math. 306(19-20), 2515–2528, special issue: Creation and Recreation: A Tribute to the Memory of Claude Berge, MR2261917 (2007e:91045).

964. W. He, X. Hou, K.-W. Lih, J. Shao, W. Wang and X. Zhu [2002], Edgepartitions of planar graphs and their game coloring numbers, J. Graph Theory 41, 307–317, MR1936946 (2003h:05153).

965. W. He, J. Wu and X. Zhu [2004], Relaxed game chromatic number of trees and outerplanar graphs, Discrete Math. 281, 209–219, MR2047768 (2005a:05088).

966. R. A. Hearn [2005], The complexity of sliding block puzzles and plank puzzles, in: Tribute to a Mathemagician, pp. 173–183, honoring Martin Gardner (B. Cipra, E. D. Demaine, M. L. Demaine and T. Rodgers, eds.), A K Peters, Wellesley, MA, pp. 93-99.

967. R. A. Hearn [2006], TipOver is NP-complete, Math. Intelligencer 28, 10– 14, Number 3, Summer 2006.

968. R. A. Hearn [2009], Amazons, Konane, and Cross Purposes are PSPACEcomplete, in: Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 287–306.

969. R. A. Hearn and E. D. Demaine [2002], The nondeterministic constraint logic model of computation: reductions and applications, in: Automata, Languages and Programming, Vol. 2380 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 401–413, MR2062475.

970. R. A. Hearn and E. D. Demaine [2005], PSPACE-completeness of slidingblock puzzles and other problems through the nondeterministic constraint logic model of computation, Theoret. Comput. Sci. 343, 72–96, special issue: Game Theory Meets Theoretical Computer Science, MR2168845 (2006d:68070).

971. R. A. Hearn and E. D. Demaine [2009], Games, puzzles, and computation, A K Peters Ltd., Wellesley, MA, 2537584.

972. O. Heden [1992], On the modular n-queen problem, Discrete Math. 102, 155–161.

973. O. Heden [1993], Maximal partial spreads and the modular n-queen problem, Discrete Math. 120, 75–91.

974. O. Heden [1995], Maximal partial spreads and the modular n-queen problem II, Discrete Math. 142, 97–106.

975. S. M. Hedetniemi, S. Hedetniemi and T. Beyer [1982], A linear algorithm for the Grundy (coloring) number of a tree, Congr. Numer. 36, 351–363.

976. S. M. Hedetniemi, S. T. Hedetniemi and R. Reynolds [1998], Combinatorial problems on chessboards, II, in: Domination in Graphs (T. W. Haynes et al., ed.), M. Dekker, NY, pp. 133–162.

977. D. Hefetz, M. Krivelevich, M. Stojaković and T. Szabó [2008], Planarity, colorability, and minor games, SIAM J. Discrete Math. 22, 194–212, MR2383236 (2009c:91029).

http://dx.doi.org/10.1137/060654414

978. D. Hefetz, M. Krivelevich, M. Stojaković and T. Szabó [2009], A sharp threshold for the Hamilton cycle Maker-Breaker game, Random Structures Algorithms 34, 112–122, MR2478541 (2009k:91035).

http://dx.doi.org/10.1002/rsa.20252

979. D. Hefetz, M. Krivelevich, M. Stojaković and T. Szabó [2009], Fast winning strategies in avoider-enforcer games, Graphs Combin. 25, 533–544, MR2575600.

http://dx.doi.org/10.1007/s00373-009-0870-8

980. D. Hefetz, M. Krivelevich, M. Stojaković and T. Szabó [2009], Fast winning strategies in Maker-Breaker games, J. Combin. Theory Ser. B 99, 39–47, MR2467817.

http://dx.doi.org/10.1016/j.jctb.2008.04.001

981. D. Hefetz, M. Krivelevich and T. Szabó [2007], Avoider-enforcer games, J. Combin. Theory Ser. A 114(5), 840–853, MR2333136.

982. P. Hegarty and U. Larsson [2006], Permutations of the natural numbers with prescribed difference multisets, Integers 6, A3, 25, 2215347 (2007a:11028).

983. P. Hein [1942], Vil de lre Polygon?, Politiken (description of Hex in this Danish newspaper of Dec. 26) .

984. G. Helleloid, M. Khalid, D. P. Moulton and P. M. Wood [2009], Graph pegging numbers, Discrete Math. 309, 1971–1985, 2510324 (2010h:05247).

http://dx.doi.org/10.1016/j.disc.2008.03.029

985. P. Henderson and R. B. Hayward [2013], A Handicap Strategy for Hex, in: Games of No Chance 4 , Cambridge University Press, to appear.

986. P. Henderson and R. B. Hayward [2013], Captured-reversible moves and star decomposition domination in Hex, Integers, Electr. J. of Combinat. Number Theory 13, #G1, 14 pp.

http://www.integers-ejcnt.org/vol3.html

987. D. Hensley [1988], A winning strategy at Taxman, Fibonacci Quart. 26, 262–270.

988. C. W. Henson [1970], Winning strategies for the ideal game, Amer. Math. Monthly 77, 836–840.

989. J. C. Hernández-Castro, I. Blasco-Lopez, J. M. Estévez-Tapiador and A. Ribagorda-Garnacho [2006], Steganography in games: A general methodology and its application to the game of Go., Computers & Security 25, 64–71.

990. C. Hernández-Cruz and H. Galeana-Sánchez [2012], k-kernels in ktransitive and k-quasi-transitive digraphs, Discrete Math. 312, 2522– 2530.

991. D. S. Herscovici, B. D. Hester and G. H. Hulbert [2012], Generalization of Graham’s pebbling conjecture, Discrete Math. 312, 2286–2293.

992. D. S. Herscovici and A. W. Higgins [1998], The pebbling number of C_{5} × C_{5}, Discrete Math. 187(1-3), 123–135, 1630692 (99d:05082).

http://dx.doi.org/10.1016/S0012-365X(97)00229-X

993. D. S. Herscovici [2003], Graham’s pebbling conjecture on products of cycles, J. Graph Theory 42(2), 141–154, 1953226 (2004j:05123).

http://dx.doi.org/10.1002/jgt.10080

994. D. S. Herscovici [2008], Graham’s pebbling conjecture on products of many cycles, Discrete Math. 308(24), 6501–6512, 2466953 (2010b:05177).

http://dx.doi.org/10.1016/j.disc.2007.12.045

995. D. S. Herscovici [2010], On graph pebbling numbers and Graham’s conjecture, Graph Theory Notes N. Y. 59, 15–21, 2849399.

996. D. S. Herscovici, B. D. Hester and G. H. Hurlbert [2011], Optimal pebbling in products of graphs, Australas. J. Combin. 50, 3–24, 2829275.

997. R. I. Hess [1999], Puzzles from around the world, in: The Mathemagician and Pied Puzzler, honoring Martin Gardner; E. Berlekamp and T. Rodgers, eds., A K Peters, Natick, MA, pp. 53-84.

998. G. Hetyei [2009], Enumeration by kernel positions, Adv. in Appl. Math. 42(4), 445–470, 2511010 (2010f:05013).

http://dx.doi.org/10.1016/j.aam.2008.11.001

999. G. Hetyei [2010], Enumeration by kernel positions for strongly Bernoulli type truncation games on words, J. Combin. Theory Ser. A 117(8), 1107– 1126, 2677677 (2011j:05007).

http://dx.doi.org/10.1016/j.jcta.2010.01.003

1000. G. A. Heuer [1982], Odds versus evens in Silverman-type games, Internat.

J. Game Theory 11, 183–194. 1001. G. A. Heuer [1989], Reduction of Silverman-like games to games on boun-

ded sets, Internat. J. Game Theory 18, 31–36.

1002. G. A. Heuer [2001], Three-part partition games on rectangles, Theoret.

Comput. Sci. (Math Games) 259, 639–661. 1003. G. A. Heuer and U. Leopold-Wildburger [1995], Silverman’s game, A

special class of two-person zero-sum games, with a foreword by Reinhard Selten, Vol. 424 of Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin.

1004. G. A. Heuer and W. D. Rieder [1988], Silverman games on disjoint discrete sets, SIAM J. Discrete Math. 1(4), 485–525, 968854 (90a:90224).

http://dx.doi.org/10.1137/0401047

1005. R. Hill [1995], Searching with lies, in: Surveys in Combinatorics, Vol. 218,

Cambridge University Press, Cambridge, pp. 41–70. 1006. R. Hill and J. P. Karim [1992], Searching with lies: the Ulam problem,

Discrete Math. 106/107, 273–283. 1007. T. P. Hill and U. Krengel [1991], Minimax-optimal stop rules and distri-

butions in secretary problems, Ann. Probab. 19, 342–353. 1008. T. P. Hill and U. Krengel [1992], On the game of Googol, Internat. J.

Game Theory 21, 151–160. 1009. P. G. Hinman [1972], Finite termination games with tie, Israel J. Math.

12, 17–22. 1010. A. M. Hinz [1989], An iterative algorithm for the tower of Hanoi with

four pegs, Computing 42, 133–140. 1011. A. M. Hinz [1989], The tower of Hanoi, Enseign. Math. 35, 289–321. 1012. A. M. Hinz [1992], Pascal’s triangle and the tower of Hanoi, Amer. Math.

Monthly 99, 538–544. 1013. A. M. Hinz [1992], Shortest paths between regular states of the tower of

Hanoi, Inform. Sci. 63, 173–181. 1014. A. M. Hinz [1999], The tower of Hanoi, Algebras and Combinatorics (K. P.

Shum, E. J. Taft and Z. X. Wan, eds.), Springer, Singapore, pp. 277–289. 1015. A. M. Hinz and D. Parisse [2002], On the planarity of Hanoi graphs, Expo.

Math. 20, 263–268, MR1924112 (2003f:05034). 1016. S. Hitotumatu [1968], Sin Ishi tori gēmu no sūri [The Theory of Nim-Like

Games], Morikita Publishing Co., Tokyo, (Japanese). 1017. S. Hitotumatu [1968], Some remarks on nim-like games, Comment. Math.

Univ. St. Paul 17, 85–98. 1018. N. B. Ho [2012], Two variants of Wythoff’s game preserving its P-

positions, J. Combin. Theory Ser. A 119(6), 1302–1314, 2915647.

http://dx.doi.org/10.1016/j.jcta.2012.03.010

1019. N. B. Ho [2012], Variations of the game 3-Euclid, Int. J. Comb. pp. Art.

ID 406250, 11, 2877573. 1020. D. G. Hoffman and P. D. Johnson [1999], Greedy colorings and the

Grundy chromatic number of the n-cube, Bull. Inst. Combin. Appl. 26, 49–57.

1021. E. J. Hoffman, J. C. Loessi and R. C. Moore [1969], Construction for the solution of the n-queens problem, Math. Mag. 42, 66–72.

1022. M. Hoffmann, J. Matoušek, Y. Okamoto and P. Zumstein [2010], Minimum and maximum against k lies, in: Algorithm theory—SWAT 2010 , Vol. 6139 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 139–149, 2678492.

1023. M. Hoffmann, J. Matoušek, Y. Okamoto and P. Zumstein [2011], The t-pebbling number is eventually linear in t, Electron. J. Combin. 18(1), Paper 153, 4, 2823374.

1024. S. Hofmann, G. Schuster and J. Steuding [2008], Euclid, Calkin & Wilf—playing with rationals, Elem. Math. 63(3), 109–117, 2424893 (2009e:91046).

http://dx.doi.org/10.4171/EM/95

1025. M. S. Hogan and D. G. Horrocks [2003], Geography played on an N-cycle times a 4-cycle, Integers, Electr. J. of Combinat. Number Theory 3, #G2, 12 pp., Comb. Games Sect., MR1985672 (2004b:91037).

http://www.integers-ejcnt.org/vol3.html

1026. J. C. Holladay [1957], Cartesian products of termination games, Ann. of Math. Stud. (Contributions to the Theory of Games), Princeton 3(39), 189–200.

1027. J. C. Holladay [1958], Matrix nim, Amer. Math. Monthly 65, 107–109. 1028. J. C. Holladay [1966], A note on the game of dots, Amer. Math. Monthly

73, 717–720. 1029. A. Holshouser and H. Reiter [2001], A generalization of Beatty’s Theorem,

Southwest J. Pure and Appl. Math., issue 2, 24–29. 1030. A. Holshouser and H. Reiter [2005], Two pile move-size dynamic Nim,

Discrete Math. Theor. Comput. Sci. 7, 1–10 (electronic), MR2164054 (2006d:91042).

1031. A. Holshouser, H. Reiter and J. Rudzinski [2003], Dynamic one-pile nim,

Fibonacci Quart. 41(3), 253–262, MR2014006 (2004i:05005). 1032. A. Holshouser, H. Reiter and J. Rudzinski [2004], Pilesize dynamic one-

pile Nim and Beatty’s theorem, Integers, Electr. J. of Combinat. Number Theory 4, #G3, 13 pp., Comb. Games Sect., MR2079848.

http://www.integers-ejcnt.org/vol4.html

1033. M. Holzer and W. Holzer [2004], TANT RIX^{TM} rotation puzzles are in-

tractable, Discrete Appl. Math. 144, 345–358, MR2098189 (2005j:94043). 1034. M. Holzer and S. Schwoon [2004], Assembling molecules in ATOMIX is

hard, Theoret. Comp. Sci. 313, 447–462, special issue of Dagstuhl Seminar “Algorithmic Combinatorial Game Theory”, Feb. 2002, MR2056938.

1035. C. W. Hong [2010], The biased, distance-restricted n-in-a-row game for small p, Theoret. Comput. Sci. 411(16-18), 1895–1897, 2650351 (2011b:91080).

http://dx.doi.org/10.1016/j.tcs.2010.02.002

1036. J. E. Hopcroft, J. T. Schwartz and M. Sharir [1984], On the complexity of motion planning for multiple independent objects: PSPACE-hardness of the ”Warehouseman’s problem”, J. Robot. Res. 3 issue 4, 76–88.

1037. B. Hopkins and J. A. Sellers [2007], Exact enumeration of Garden of Eden partitions, de Gruyter, pp. 299–303, Proc. Integers Conference, Carrollton, Georgia, October 27-30,2005, in celebration of the 70th birthday of Ronald Graham. B. Landman, M. Nathanson, J. Nešetřil, R. Nowakowski, C. Pomerance eds., appeared also in Integers, Electr. J. of Combinat. Number Theory 7(20), special volume in honor of Ron Graham, #A19, 5 pp., MR2337053.

http://www.integers-ejcnt.org/vol7(2).html

1038. E. Hordern [1986], Sliding Piece Puzzles, Oxford University Press, Oxford. 1039. D. Horrocks [2010], Winning positions in simplicial Nim, Electron. J.

Combin. 17(1), Research Paper 84, 13, 2661387 (2012a:91047).

http://www.combinatorics.org/Volume_17/Abstracts/v17i1r84.
html

1040. D. G. Horrocks and R. J. Nowakowski [2003], Regularity in the G− sequences of octal games with a pass, Integers, Electr. J. of Combinat. Number Theory 3, #G1, 10 pp., Comb. Games Sect., MR1985671 (2004d:91049).

http://www.integers-ejcnt.org/vol3.html

1041. D. G. Horrocks and M. A. Trenton [2008], Subtraction with a Muller twist, Integers, Electr. J of Combinat. Number Theory 8, G05, 12, MR2425634 (2009h:91051).

1042. D. Howard and C. Smyth [2012], Revolutianaries and spies, Discrete

Math. 312, 3384–3391. 1043. S. Howse and R. J. Nowakoski [2004], Periodicity and arithmetic-

periodicity in hexadecimal games, Theoret. Comp. Sci. 313, 463–472, special issue of Dagstuhl Seminar “Algorithmic Combinatorial Game Theory”, Feb. 2002, MR2056939 (2005f:91037).

1044. M. Y. Hsieh and S.-C. Tsai [2007], On the fairness and complexity of generalized k-in-a-row games, Theoret. Comput. Sci. 385, 88–100, MR2356244.

1045. S. Huddleston and J. Shurman [2002], Transfinite Chomp, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 183–212, MR1973013 (2004b:91046).

1046. Y.-C. Hung, R. W. Chen, A. Zame and M.-R. Chen [2010], A note on the first occurrence of strings, Electron. J. Combin. 17(1), Note 5, 8, 2587755 (2011d:05013).

http://www.combinatorics.org/Volume_17/Abstracts/v17i1n5.
html

1047. P. Hunter and S. Kreutzer [2008], Digraph measures: Kelly decompositions, games, and orderings, Theoret. Comput. Sci. 399(3), 206–219, 2419778 (2009g:05169).

http://dx.doi.org/10.1016/j.tcs.2008.02.038

1048. G. H. Hurlbert [1998], Two pebbling theorems, Congr. Numer. 135, 55– 63, Proc. 29-th Southeastern Internat. Conf. on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1998).

1049. G. H. Hurlbert [1999], A survey of graph pebbling, Congr. Numer. 139, 41–64, Proc. 30-th Southeastern Internat. Conf. on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1999).

1050. G. Iba and J. Tanton [2003], Candy sharing, Amer. Math. Monthly 110,

25–35, MR1952745. 1051. K. Igusa [1985], Solution of the Bulgarian solitaire conjecture, Math. Mag.

58(5), 259–271, MR810147 (87c:00003). 1052. E. J. Ionascu, D. Pritikin and S. E. Wright [2008], k-dependence and

domination in kings graphs, Amer. Math. Monthly 115, 820–836, 2463293 (2009i:05180).

1053. J. Isbell [1992], The Gordon game of a finite group, Amer. Math. Monthly

99, 567–569. 1054. V. Isler, S. Kannan and S. Khanna [2006], Randomized pursuit-evasion

with local visibility, SIAM J. Discrete Math. 20, 26–41 (electronic), MR2257242 (2007h:91038).

1055. V. Isler and N. Karnad [2008], The role of information in the cop-robber game, Theoret. Comput. Sci. 399(3), 179–190, 2419776 (2009f:91017).

http://dx.doi.org/10.1016/j.tcs.2008.02.041

1056. H. Ito, G. Nakamura and S. Takata [2007], Winning ways of weighted poset games, Graphs Combin. 23(suppl. 1), 291–306, 2320636 (2008c:91040).

http://dx.doi.org/10.1007/s00373-007-0710-7

1057. O. Itzinger [1977], The South American game, Math. Mag. 50, 17–21. 1058. Y. Iwasaki [2009], Solution for the Tower of Hanoi problem with four

pegs, Adv. Appl. Discrete Math. 4(2), 95–104, 2590297. 1059. S. Iwata and T. Kasai [1994], The Othello game on an n × n board is

PSPACE-complete, Theoret. Comput. Sci. (Math Games) 123, 329–340. 1060. H. Jacob and H. Meyniel [1996], About quasi-kernels in a digraph, Dis-

crete Math. 154, 279–280, 1395467 (97a:05093).

http://dx.doi.org/10.1016/0012-365X(93)E0035-3

1061. C. F. A. Jaenisch [1862], Traité des Applications de l’Analyse mathématiques au Jeu des Echecs, Petrograd, three volumes (Carl Friedrich Andreyevich Jaenisch from St Petersburg [changed its name to Petrograd, then to Leningrad, and then back to St Petersburg] is also known by his cyrillic transliteration ”Yanich”, or in the French form: de J, or German form: von J).

1062. J. James and M. Schlatter [2008], Some observations and solutions to short and long global nim, Integers, Electr. J of Combinat. Number Theory 8, G01, 14, MR2373090 (2008k:91051).

1063. J. Jeffs and S. Seager [1995], The chip firing game on n-cycles, Graphs

Combin. 11, 59–67. 1064. T. A. Jenkyns and J. P. Mayberry [1980], The skeleton of an impartial game and the Nim-function of Moore’s Nim_{k}, Internat. J. Game Theory 9, 51–63.

1065. T. R. Jensen and B. Toft [1995], Graph Coloring Problems, Wiley-Inter-science Series in Discrete Mathematics and Optimization, Wiley, New York, NY.

1066. Y. Jiao [2013], On the Sprague-Grundy values of the F-Wythoff game, Electr. J. Combin. 20(1), #14, 12 pp.

http://www.combinatorics.org/

1067. L. Y. Jin and J. Nievergelt [2008], Tigers and Goats is a draw, in: Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 163–176.

1068. D. S. Johnson [1983], The NP-Completeness Column: An Ongoing Guide, J. Algorithms 4, 397–411, 9th quarterly column (games); the column started in 1981; a further games update appeared in vol. 5, 10th column, pp. 154-155.

1069. W. W. Johnson [1879], Notes on the ”15” puzzle, Amer. J. Math. 2,

397–399. 1070. J. P. Jones [1982], Some undecidable determined games, Internat. J.

Game Theory 11, 63–70. 1071. J. P. Jones and A. S. Fraenkel [1995], Complexities of winning strategies

in diophantine games, J. Complexity 11, 435–455. 1072. D. Joyner [2006], Mathematics of Ghaly’s machine, Integers, Electr. J. of

Combinat. Number Theory 6, #G01, 27 pp., Comb. Games Sect.

http://www.integers-ejcnt.org/vol6.html

1073. M. Kac [1974], Hugo Steinhaus, a reminiscence and a tribute, Amer. Math.

Monthly 81, 572–581 (p. 577). 1074. J. Kahane and A. S. Fraenkel [1987], k-Welter—a generalization of Wel-

ter’s game, J. Combin. Theory Ser. A 46(1), 1–20, 899899 (88k:90221).

http://dx.doi.org/10.1016/0097-3165(87)90073-2

1075. J. Kahane and A. J. Ryba [2001], The Hexad game, Electr. J. Combin. 8(2), #R11, 9 pp., Volume in honor of Aviezri S. Fraenkel, MR1853262 (2002h:91031).

http://www.combinatorics.org/

1076. J. Kahn, J. C. Lagarias and H. S. Witsenhausen [1987], Single-suit twoperson card play, Internat. J. Game Theory 16, 291–320, MR0918819 (88m:90162).

1077. J. Kahn, J. C. Lagarias and H. S. Witsenhausen [1988], Single-suit two-

person card play, II. Dominance, Order 5, 45–60, MR0953941 (89j:90279). 1078. J. Kahn, J. C. Lagarias and H. S. Witsenhausen [1989], On Lasker’s card

game, in: Differential Games and Applications, Lecture Notes in Control and Information Sciences (T. S. Başar and P. Bernhard, eds.), Vol. 119, Springer Verlag, Berlin, pp. 1–8, MR1230186.

1079. J. Kahn, J. C. Lagarias and H. S. Witsenhausen [1989], Single-suit twoperson card play, III. The misère game, SIAM J. Disc. Math. 2, 329–343, MR1002697 (90g:90197).

1080. L. Kalmár [1928], Zur Theorie der abstrakten Spiele, Acta Sci. Math.

Univ. Szeged 4, 65–85. 1081. B. Kalyanasundram [1991], On the power of white pebbles, Combinatorica

11, 157–171. 1082. B. Kalyanasundram and G. Schnitger [1988], On the power of white peb-

bles, Proc. 20th Ann. ACM Symp. Theory of Computing (Chicago, IL, 1988), Assoc. Comput. Mach., New York, NY, pp. 258–266.

1083. J. H. Kan [1994], (0, 1) matrices, combinatorial games and Ramsey prob-

lems, Math. Appl. (Wuhan) 7, 97–101, (Chinese; English summary). 1084. D. M. Kane [2010], On solving games constructed using both short and

long conjunctive sums, Integers 10, G04, 849–878, 2797777.

http://dx.doi.org/10.1515/INTEG.2010.104

1085. M. Kano [1983], Cycle games and cycle cut games, Combinatorica 3(2), 201–206, 726458 (85d:90144).

http://dx.doi.org/10.1007/BF02579294

1086. M. Kano [1993], An edge-removing game on a graph (a generalization of Nim and Kayles), in: Optimal Combinatorial Structures on Discrete Mathematical Models (in Japanese, Kyoto, 1992), Sūrikaisekikenkyūsho Kōkyūroku, pp. 82–90, MR1259331 (94m:90132).

1087. M. Kano [1996], Edge-removing games of star type, Discrete Math. 151,

113–119. 1088. M. Kano, T. Sasaki, H. Fujita and S. Hoshi [1993], Life games of Ibadai

type, in: Combinatorial Structure in Mathematical Models (in Japanese, Kyoto, 1993), Sūrikaisekikenkyūsho Kōkyūroku, pp. 108–117.

1089. S. Kanungo and R. M. Low [2007], Further analysis on the “king and rook vs. king on a quarter-infinite board” problem, Integers 7, G09, 7, 2373122.

1090. K.-Y. Kao [2005], Sumbers – sums of ups and downs, Integers, Electr. J. of Combinat. Number Theory 5, #G01, 13 pp., Comb. Games Sect., MR2139164 (2005k:91081).

http://www.integers-ejcnt.org/vol5.html

1091. K.-Y. Kao, I.-C. Wu, Y.-C. Shan and H.-H. Lin [2010], Chilled Domineering, Technologies and Applications of Artificial Intelligence, International Conference on 0, 427–432.

1092. K.-Y. Kao, I.-C. Wu, Y.-C. Shan and S.-J. Yen [2012], Selection search for mean and temparature of multi-branch combinatorial games, ICGA J. 35, 157–176.

1093. R. M. Karp and Y. Zhang [1989], On parallel evaluation of game trees,

Proc. ACM Symp. Parallel Algorithms and Architectures, pp. 409–420. 1094. T. Kasai, A. Adachi and S. Iwata [1979], Classes of pebble games and

complete problems, SIAM J. Comput. 8(4), 574–586, 573848 (82a:68075).

http://dx.doi.org/10.1137/0208046

1095. N. Kawanaka [2001], Sato-Welter game and Kac-Moody Lie algebras (English), Sūrikaisekikenkyūsho Kōkyūroku (1190), 95–106, Topics in combinatorial representation theory (Japanese) (Kyoto, 2000), 1847734.

1096. Y. Kawano [1996], Using similar positions to search game trees, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 193–202.

1097. R. Kaye [2000], Minesweeper is NP-complete, Math. Intelligencer 22(2), 9–15, 1764264.

http://dx.doi.org/10.1007/BF03025367

1098. M. D. Kearse and P. B. Gibbons [2001], Computational methods and new results for chessboard problems, Australas. J. Combin. 23, 253–284, MR1815018 (2001m:05190).

1099. M. D. Kearse and P. B. Gibbons [2002], A new lower bound on upper irredundance in the queens’ graph, Discrete Math. 256, 225–242, MR1927068 (2003g:05098).

1100. A. Kehagias and P. Prałat [2012], Some remarks on cops and drunk robbers, Theoret. Comput. Sci. 463, 133–147, 2992504.

http://dx.doi.org/10.1016/j.tcs.2012.08.016

1101. J. C. Kenyon [1967], A Nim-like game with period 349, Res. Paper No. 13,

Univ. of Calgary, Math. Dept. 1102. J. C. Kenyon [1967], Nim-like games and the Sprague–Grundy theory,

M.Sc. Thesis, Univ. of Calgary. 1103. B. Kerst [1933], Mathematische Spiele, Reprinted by Dr. Martin Sa̋ndig

oHG, Wiesbaden 1968. 1104. T. Khovanova and J. B. Lewis [2011], Baron Münchhausen redeems him-

self: bounds for a coin-weighing puzzle, Electron. J. Combin. 18(1), Paper 37, 14, 2776813.

1105. J. Y. Kim [2011], The incidence game chromatic number of paths and subgraphs of wheels, Discrete Appl. Math. 159(8), 683–694, 2782626 (2012b:05121).

http://dx.doi.org/10.1016/j.dam.2010.01.001

1106. H. A. Kierstead [2000], A simple competitive graph coloring algorithm, J. Combin. Theory Ser. B 78, 57–68, MR1737624 (2001k:05074).

http://dx.doi.org/10.1006/jctb.1999.1927

1107. H. A. Kierstead [2005], Asymmetric graph coloring games, J. Graph The-

ory 48(3), 169–185, MR2116838 (2006c:91033). 1108. H. A. Kierstead [2006], Weak acyclic coloring and asymmetric coloring

games, Discrete Math. 306(7), 673–677, MR2215592 (2006j:05069).

http://dx.doi.org/10.1016/j.disc.2004.07.042

1109. H. A. Kierstead and A. V. Kostochka [2009], Efficient graph packing via game colouring, Combin. Probab. Comput. 18(5), 765–774, 2534268 (2010j:05322).

http://dx.doi.org/10.1017/S0963548309009973

1110. H. Kierstead, B. Mohar, S. Špacapan, D. Yang and X. Zhu [2009], The two-coloring number and degenerate colorings of planar graphs, SIAM J. Discrete Math. 23(3), 1548–1560, 2556548 (2011b:05073).

http://dx.doi.org/10.1137/070703697

1111. H. A. Kierstead and P. H. Nyikos [1988], Racing pawn games, Congr. Numer. 67, 257–264, Nineteenth Southeastern Conference on Combinatorics, Graph Theory, and Computing (Baton Rouge, LA, 1988), MR992938 (90c:90245).

1112. H. A. Kierstead and W. T. Trotter [1994], Planar graph coloring with an uncooperative partner, J. Graph Theory 18, 569–584, Volume in honor of Aviezri S. Fraenkel, MR1292976 (95f:05043).

1113. H. A. Kierstead and W. T. Trotter [2001], Competitive colorings of oriented graphs, Electr. J. Combin. 8(2), #R12, 15 pp., Volume in honor of Aviezri S. Fraenkel, MR1853263 (2002g:05083).

http://www.combinatorics.org/

1114. H. A. Kierstead and Zs. Tuza [2003], Marking games and the oriented game chromatic number of partial k-trees, Graphs Combin. 19, 121–129, MR1974374 (2003m:05069).

1115. H. A. Kierstead and D. Yang [2003], Orderings on graphs and game coloring number, Order 20(3), 255–264 (2004), MR2064049 (2005a:05091).

http://dx.doi.org/10.1023/B:ORDE.0000026489.93166.cb

1116. H. A. Kierstead and D. Yang [2005], Very asymmetric marking games,

Order 22(2), 93–107 (2006), MR2207192 (2007d:91045). 1117. H. A. Kierstead, C.-Y. Yang, D. Yang and X. Zhu [2012], Adapted game

colouring of graphs, European J. Combin. 33(4), 435–445, 2864427.

http://dx.doi.org/10.1016/j.ejc.2011.11.001

1118. Y. Kim [1996], New values in domineering, Theoret. Comput. Sci. (Math

Games) 156, 263–280. 1119. C. Kimberling [2007], Complementary equations, J. Integer Seq. 10(1),

Article 07.1.4, 14 pp. (electronic), MR2268455.

http://www.cs.uwaterloo.ca/journals/JIS/VOL10/Kimberling/
kimberling26.pdf

1120. C. Kimberling [2007], The equation m^{2} − 4k = 5n^{2} and unique representations of positive integers, Fibonacci Quart. 45(4), 304–312 (2008), 2478613 (2009m:11040).

1121. C. Kimberling [2008], Complementary equations and Wythoff sequences,

J. Integer Seq. 11(3), Article 08.3.3, 8, 2429960 (2009f:11030). 1122. H. Kinder [1973], Gewinnstrategien des Anziehenden in einigen Spielen

auf Graphen, Arch. Math. 24, 332–336. 1123. M. A. Kiwi, R. Ndoundam, M. Tchuente and E. Goles [1994], No poly-

nomial bound for the period of the parallel chip firing game on graphs, Theoret. Comput. Sci. 136, 527–532.

1124. D. A. Klarner, ed. [1998], Mathematical recreations. A collection in honor of Martin Gardner, Dover, Mineola, NY, Corrected reprint of The Math-

ematical Gardner, Wadsworth Internat., Belmont, CA, 1981. 1125. S. Klavžar and U. Milutinović [1997], Graphs S(n, k) and a variant of the

tower of Hanoi problem, Czechoslovak Math. J. 47, 95–104, MR1435608 (97k:05061).

1126. S. Klavžar and U. Milutinović [2002], Simple explicit formulas for the Frame-Stewart numbers, Ann. Comb. 6, 157–167, MR1955516 (2003k:05004).

1127. S. Klavžar, U. Milutinović and C. Petr [2001], Combinatorics of topmost discs of multi-peg tower of Hanoi problem, Ars Combinatoria 59, 55–64, MR1832197 (2002b:05013).

1128. S. Klavžar, U. Milutinović and C. Petr [2002], On the Frame-Stewart algorithm for the multi-peg tower of Hanoi problem, Discrete Appl. Math. 120, 141–157, MR1966398.

1129. M. M. Klawe [1985], A tight bound for black and white pebbles on the

pyramids, J. Assoc. Comput. Mach. 32, 218–228. 1130. C. S. Klein and S. Minsker [1993], The super towers of Hanoi problem:

large rings on small rings, Discrete Math. 114, 283–295. 1131. D. J. Kleitman and B. L. Rothschild [1972], A generalization of Kaplan-

sky’s game, Discrete Math. 2, 173–178. 1132. O. Kloster [2007], A solution to the angel problem, Theoret. Comput. Sci.

389(1-2), 152–161, 2363369 (2008j:91039).

http://dx.doi.org/10.1016/j.tcs.2007.08.006

1133. T. Kløve [1977], The modular n-queen problem, Discrete Math. 19, 289–

291. 1134. T. Kløve [1981], The modular n-queen problem II, Discrete Math. 36,

33–48. 1135. K. Knauer, P. Micek and T. Ueckerdt [2011], How to eat 4/9 of a pizza,

Discrete Math. 311(16), 1635–1645, 2806028 (2012e:91185).

http://dx.doi.org/10.1016/j.disc.2011.03.015

1136. A. Knopfmacher and H. Prodinger [2001], A Simple Card Guessing Game Revisited, Electr. J. Combin. 8(2), #R13, 9 pp., Volume in honor of Aviezri S. Fraenkel, MR1853264 (2002g:05007).

http://www.combinatorics.org/

1137. M. Knor [1996], On Ramsey-type games for graphs, Australas. J. Combin.

14, 199–206. 1138. D. E. Knuth [1974], Surreal Numbers, Addison-Wesley, Reading, MA. 1139. D. E. Knuth [1976], The computer as Master Mind, J. Recr. Math. 9,

1–6. 1140. D. E. Knuth [1977], Are toy problems useful?, Popular Computing 5 issue

1, 3-10; continued in 5 issue 2, 3-7. 1141. D. E. Knuth [1993], The Stanford Graph Base: A Platform for Combina-

torial Computing, ACM Press, New York. 1142. D. E. Knuth [1994], Leaper graphs, Math. Gazette 78(483), 274–297.

1143. P. Komjáth [1984], A simple strategy for the Ramsey-game, Studia Sci.

Math. Hung. 19, 231–232. 1144. S. C. Kontogiannis, P. N. Panagopoulou and P. G. Spirakis [2009], Poly-

nomial algorithms for approximating Nash equilibria of bimatrix games, Theoret. Comput. Sci. 410(17), 1599–1606, 2510266 (2010h:68217).

http://dx.doi.org/10.1016/j.tcs.2008.12.033

1145. G. Kortsarz [2007], A lower bound for approximating the Grundy number, Discrete Math. Theor. Comput. Sci. 9(1), 7–21 (electronic), 2282196 (2007m:05092).

1146. A. Kotzig [1946], O k-posunutiach (On k-translations; in Slovakian), Časop. pro Pěst. Mat. a Fys. 71, 55–61, extended abstract in French, pp. 62–66.

1147. G. Kowalewski [1930], Alte und neue mathematische Spiele, Reprinted by

Dr. Martin Sa̋ndig oHG, Wiesbaden 1968. 1148. K. Koyama and T. W. Lai [1993], An optimal Mastermind strategy, J.

Recr. Math. 25, 251–256. 1149. M. Kraitchik [1953], Mathematical Recreations, Dover, New York, NY,

2nd edn. 1150. D. Král, V. Majerech, J. Sgall, T. Tichý and G. Woeginger [2004], It is

tough to be a plumber, Theoret. Comp. Sci. 313, 473–484, special issue of Dagstuhl Seminar “Algorithmic Combinatorial Game Theory”, Feb. 2002, MR2056940.

1151. W. O. Krawec [2012], Analyzing n-player impartial games, Int. J. Game

Theory 41, 345–367. 1152. M. Krivelevich and T. Szabó [2008], Biased positional games and small

hypergraphs with large covers, Electron. J. Combin. 15(1), Research Paper 70, 13, 2411447 (2009h:91047).

http://www.combinatorics.org/Volume_15/Abstracts/v15i1r70.
html

1153. I. Kříž [1985], Changes of the outcome of combinatorial games with differing number of prohibited repetitions, Comment. Math. Univ. Carolin. 26(2), 363–372, 803934 (87h:90274).

1154. K. Kruczek and E. Sundberg [2008], A pairing strategy for tic-tac-toe on the integer lattice with numerous directions, Electron. J. Combin. 15(1), Note 42, 6, 2465759 (2010c:91029).

http://www.combinatorics.org/Volume_15/Abstracts/v15i1n42.
html

1155. K. Kruczek and E. Sundberg [2010], Potential-based strategies for tic-tac-toe on the integer lattice with numerous directions, Electron. J. Combin. 17(1), Research Paper 5, 15, 2578900 (2011g:05204).

http://www.combinatorics.org/Volume_17/Abstracts/v17i1r5.
html

1156. B. Kummer [1980], Spiele auf Graphen, Internat. Series of Numerical Mathematics, Birkhäuser Verlag, Basel.

1157. D. Kunkle and G. Cooperman [2007], Twenty-six moves suffice for Rubik’s cube, in: ISSAC 2007 , ACM, New York, pp. 235–242, 2402267 (2009c:20005).

http://dx.doi.org/10.1145/1277548.1277581

1158. D. Kunkle and G. Cooperman [2009], Harnessing parallel disks to solve Rubik’s cube, J. Symbolic Comput. 44(7), 872–890, 2522588 (2010g:05015).

http://dx.doi.org/10.1016/j.jsc.2008.04.013

1159. M. Kutz [2005], Conway’s angel in three dimensions, Theoret. Comput.

Sci. 349, 443–451, MR2183168 (2006h:91045). 1160. M. Kutz and A. Pór [2005], Angel, Devil, and King, in: Computing and

Combinatorics, Vol. 3595 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 925–934, Proc. COCOON, MR2190915 (2006g:91043).

1161. M. Lachmann, C. Moore and I. Rapaport [2002], Who wins Domineering on rectangular boards?, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 307–315, MR1973019 (2004b:91047).

1162. R. E. Ladner and J. K. Norman [1985], Solitaire automata, J. Comput.

System Sci. 30, 116–129, MR 86i:68032. 1163. J. C. Lagarias [1977], Discrete balancing games, Bull. Inst. Math. Acad.

Sinica 5, 363–373. 1164. J. Lagarias and D. Sleator [1999], Who wins misère Hex?, in: The Math-

emagician and Pied Puzzler, honoring Martin Gardner; E. Berlekamp and T. Rodgers, eds., A K Peters, Natick, MA, pp. 237-240.

1165. S. P. Lalley [1988], A one-dimensional infiltration game, Naval Res. Lo-

gistics 35, 441–446. 1166. P. C. B. Lam, W. C. Shiu and B. Xu [1999], Edge game-coloring of graphs,

Graph Theory Notes N. Y. 37, 17–19, MR1724310. 1167. T. K. Lam [1997], Connected sprouts, Amer. Math. Monthly 104, 116–

119. 1168. H. A. Landman [1996], Eyespace values in Go, in: Games of No Chance,

Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 227–257, MR1427967 (97j:90100).

1169. H. Landman [2002], A simple FSM-based proof of the additive periodicity of the Sprague-Grundy function of Wythoff’s game, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 383–386, MR1973106 (2004b:91048).

1170. L. Larson [1977], A theorem about primes proved on a chessboard, Math.

Mag. 50, 69–74. 1171. U. Larsson [2009], 2-pile Nim with a restricted number of move-size im-

itations, Integers 9, G04, 671–690, With an appendix by Peter Hegarty, 2592547 (2011e:91054).

http://dx.doi.org/10.1515/INTEG.2009.053

1172. U. Larsson [2011], Blocking Wythoff nim, Electron. J. Combin. 18(1),

Paper 120, 18, 2811089. 1173. U. Larsson [2012], A Generalized Diagonal Wythoff Nim, Integers, Electr.

J. of Combinat. Number Theory 12, #G02, 24 pp., Comb. Games Sect.

http://www.integers-ejcnt.org/vol12.html

1174. U. Larsson [2012], The *-operator and invariant subtraction games, The-

oret. Comput. Sci. 422(1), 52–58. 1175. U. Larsson [2013], Restrictions of m-Wythoff Nim and p-complementary

Beatty Sequences, in: Games of No Chance 4 , Cambridge University Press, to appear.

1176. U. Larsson, P. Hegarty and A. S. Fraenkel [2011], Invariant and dual subtraction games resolving the Duchêne-Rigo conjecture, Theoret. Comput. Sci. 412(8-10), 729–735, 2796920 (2012d:91053).

http://dx.doi.org/10.1016/j.tcs.2010.11.015

1177. R. Laskar, A. McRae and C. Wallis [2003], Domination in triangulated chessboard graphs, Proceedings of the Thirty-Fourth Southeastern International Conference on Combinatorics, Graph Theory and Computing, Vol. 163, pp. 107–123, 2050563.

1178. R. Laskar and C. Wallis [1994], Domination parameters of graphs of threeclass association schemes and variations of chessboard graphs, Proceedings of the Twenty-fifth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1994), Vol. 100, pp. 199–213, 1382320 (96k:05212).

1179. R. Laskar and C. Wallis [1999], Chessboard graphs, related designs, and domination parameters, J. Statist. Plann. Inference 76(1-2), 285–294, 1673351 (2000g:05042).

http://dx.doi.org/10.1016/S0378-3758(98)00132-3

1180. R. Laskar and C. Wallis [2004], Domination and independence in the graph of the T_{3} association scheme and related chessboard graphs, Proceedings of the Thirty-Fifth Southeastern International Conference on Combinatorics, Graph Theory and Computing, Vol. 167, pp. 109–120, 2122026 (2005i:05134).

1181. E. Lasker [1931], Brettspiele der Völker, Rätsel und mathematische Spiele,

Berlin. 1182. M. Latapy and C. Magnien [2002], Coding distributive lattices with

edge firing games, Inform. Process. Lett. 83, 125–128, MR1837204 (2002h:37022).

1183. M. Latapy and H. D. Phan [2001], The lattice structure of chip firing games and related models, Phys. D 155, 69–82, MR1837204 (2002h:37022).

1184. I. Lavalée [1985], Note sur le problème des tours d’Hanoï, Rev. Roumaine Math. Pures Appl. 30, 433–438.

1185. E. L. Lawler and S. Sarkissian [1995], An algorithm for “Ulam’s game” and its application to error correcting codes, Inform. Process. Lett. 56, 89–93.

1186. A. J. Lazarus, D. E. Loeb, J. G. Propp, W. R. Stromquist and D. Ullman [1999], Combinatorial games under auction play, Games Econom. Behav. 27, 229–264, MR1685133 (2001f:91023).

1187. A. J. Lazarus, D. E. Loeb, J. G. Propp and D. Ullman [1996], Richman Games, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 439–449, MR1427981 (97j:90101).

1188. S.-G. Lee and J.-M. Yang [2006], Linear algebraic approach on real σ-game, J. Appl. Math. Comput. 21(1-2), 295–305, MR2218803 (2006k:91056).

1189. D. B. Leep and G. Myerson [1999], Marriage, magic and solitaire, Amer.

Math. Monthly 106, 419–429. 1190. A. Lehman [1964], A solution of the Shannon switching game, J. Soc.

Indust. Appl. Math. 12, 687–725, 0173250 (30 #3463). 1191. E. L. Leiss [1983], On restricted Hanoi problems, J. Combin. Inform.

System Sci. 8, 277–285, MR783767 (86i:05072). 1192. E. Leiss [1983], Solving the “Towers of Hanoi” on graphs, J. Combin.

Inform. System Sci. 8, 81–89, MR783741 (86i:05071). 1193. E. L. Leiss [1984], Finite Hanoi problems: how many discs can be han-

dled?, Congr. Numer. 44, 221–229, Proc. 15th Southeastern Internat. Conf. on Combinatorics, Graph Theory and Computing (Baton Rouge, LA, 1984), MR777543 (87b:05062).

1194. J. Lemoine and S. Viennot [2012], Nimbers are inevitable, Theoret. Com-

put. Sci. 462, 70–79. 1195. J. Lemoine and S. Viennot [2013], Computer Analysis of Sprouts with

Nimbers, in: Games of No Chance 4 , Cambridge University Press, to appear.

1196. T. Lengauer and R. Tarjan [1980], The space complexity of pebble games

on trees, Inform. Process. Lett. 10, 184–188. 1197. T. Lengauer and R. Tarjan [1982], Asymptotically tight bounds on time-

space trade-offs in a pebble game, J. Assoc. Comput. Mach. 29, 1087– 1130.

1198. T. Lengyel [2003], A Nim-type game and continued fractions, Fibonacci

Quart. 41, 310–320, MR2022411. 1199. J. H. W. Lenstra [1977], On the algebraic closure of two, Proc. Kon.

Nederl. Akad. Wetensch. (Ser. A) 80, 389–396. 1200. J. H. W. Lenstra [1977/1978], Nim multiplication, Séminaire de Théorie

des Nombres No. 11, Université de Bordeaux, France. 1201. L. Levine [2006], Fractal sequences and restricted Nim, Ars Combin. 80,

113–127, MR2243082 (2007b:91029).

1202. D. N. L. Levy, H. J. Berliner and E. O. Thorpe [2009], Computer Games,

I, II , Ishi Press, appeared first in 1988, by Levy, Springer. 1203. J. Lewin [1986], The lion and man problem revisited, J. Optimization

Theory and Applications 49, 411–430. 1204. T. Lewis and S. Willard [1980], The rotating table, Math. Mag. 53, 174–

179. 1205. C.-K. Li and I. Nelson [1998], Perfect codes on the towers of Hanoi graph,

Bull. Austral. Math. Soc. 57, 367–376. 1206. S.-Y. R. Li [1974], Generalized impartial games, Internat. J. Game Theory

3, 169–184, 0384170 (52 #5047). 1207. S. Y. R. Li [1976], Sums of Zuchswang games, J. Combinatorial Theory

Ser. A 21(1), 52–67, 0426869 (54 #14802). 1208. S.-Y. R. Li [1977], N-person nim and N-person Moore’s games, Internat.

J. Game Theory 7, 31–36. 1209. W. Li, D. Wu and F. Pan [2012], A construction for doubly pandiagonal

magic squares, Discrete Math. 312(2), 479–485, 2852609.

http://dx.doi.org/10.1016/j.disc.2011.09.031

1210. D. Lichtenstein [1982], Planar formulae and their uses, SIAM J. Comput.

11, 329–343. 1211. D. Lichtenstein and M. Sipser [1980], Go is Polynomial-Space hard, J.

Assoc. Comput. Mach. 27, 393–401, earlier version appeared in Proc. 19th Ann. Symp. Foundations of Computer Science (Ann Arbor, MI, Oct. 1978), IEEE Computer Soc., Long Beach, CA, 1978, pp. 48–54.

1212. H. Liebeck [1971], Some generalizations of the 14-15 puzzle, Math. Mag.

44, 185–189. 1213. C.-W. Lim [2005], Partial Nim, Integers, Electr. J. of Combinat. Number

Theory 5, #G02, 9 pp., Comb. Games Sect., MR2139165 (2005m:91046).

http://www.integers-ejcnt.org/vol5.html

1214. W. Lin and X. Zhu [2009], Circular game chromatic number of graphs, Discrete Math. 309(13), 4495–4501, 2519188 (2010i:05127).

http://dx.doi.org/10.1016/j.disc.2009.02.011

1215. W. A. Liu, H. Li and B. Li [2011], A restricted version of Wythoff’s game,

Electron. J. Combin. 18(1), Paper 207, 17, 2853064. 1216. W. A. Liu, H. Li, Y. Ma and B. Li [2012], On supplements of 2×m board

in Toppling Towers, Integers, Electr. J. of Combinat. Number Theory 12, #G4, 19 pp.

1217. C. Löding and P. Rohde [2003], Solving the sabotage game is PSPACEhard, in: Mathematical Foundations of Computer Science 2003 , Vol. 2747 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 531–540, MR2081603.

1218. D. E. Loeb [1995], How to win at Nim, UMAP J. 16, 367–388. 1219. D. E. Loeb [1996], Stable winning coalitions, in: Games of No Chance,

Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 451–471.

1220. L. Longpré and P. McKenzie [2009], The complexity of solitaire, Theoret. Comput. Sci. 410(50), 5252–5260, Appeared first in Mathematical foundations of computer science 2007, 182193, Lecture Notes in Comput. Sci., 4708, Springer, Berlin, 2007, 2573977 (2011b:91082).

http://dx.doi.org/10.1016/j.tcs.2009.08.027

1221. A. M. Loosen [2008], Directional phutball, Atl. Electron. J. Math. 3, 30–

45, 2827227. 1222. J. A. M. Lopez [1991], A prolog Mastermind program, J. Recr. Math. 23,

81–93. 1223. R. M. Low and M. Stamp [2006], King and rook vs. king on a quarter-

infinite board, Integers, Electr. J. of Combinat. Number Theory 6, #G3, 8 pp., MR2247807 (2007c:91038).

http://www.integers-ejcnt.org/vol6.html

1224. S. Loyd [1914], Cyclopedia of Puzzles and Tricks, Franklin Bigelow Corporation, Morningside Press, NY, reissued and edited by M. Gardner under the name The Mathematical Puzzles of Sam Loyd (two volumes), Dover, New York, NY, 1959.

1225. X. Lu [1986], A Hamiltonian game, J. Math. Res. Exposition (English

Ed.) 1, 101–106. 1226. X. Lu [1991], A matching game, Discrete Math. 94, 199–207. 1227. X. Lu [1992], A characterization on n-critical economical generalized tic-

tac-toe games, Discrete Math. 110, 197–203. 1228. X. Lu [1992], Hamiltonian games, J. Combin. Theory (Ser. B) 55, 18–32. 1229. X. Lu [1995], A Hamiltonian game on K_{n,n}, Discrete Math. 142, 185–191. 1230. X. Lu [1995], A note on biased and non-biased games, Discrete Appl.

Math. 60, 285–291, Presented at ARIDAM VI and VII (New Brunswick, NJ, 1991/1992).

1231. X.-M. Lu [1986], Towers of Hanoi graphs, Intern. J. Comput. Math. 19,

23–38. 1232. X.-M. Lu [1988], Towers of Hanoi problem with arbitrary k ≥ 3 pegs,

Intern. J. Comput. Math. 24, 39–54. 1233. X.-M. Lu [1989], An iterative solution for the 4-peg towers of Hanoi,

Comput. J. 32, 187–189. 1234. X.-M. Lu and T. S. Dillon [1994], A note on parallelism for the towers of

Hanoi, Math. Comput. Modelling 20 issue 3, 1–6. 1235. X.-M. Lu and T. S. Dillon [1995], Parallelism for multipeg towers of Hanoi,

Math. Comput. Modelling 21 issue 3, 3–17. 1236. X.-M. Lu and T. S. Dillon [1996], Nonrecursive solution to parallel multi-

peg towers of Hanoi: a decomposition approach, Math. Comput. Modelling 24 issue 3, 29–35.

1237. É. Lucas [1960], Récréations Mathématiques, Vol. I – IV, A. Blanchard, Paris. Previous editions: Gauthier-Villars, Paris, 1891–1894.

1238. É. Lucas [1974], Introduction aux Récréations Mathématiques: L’Arithmétique Amusante, reprinted by A. Blanchard, Paris. Originally published by A. Blanchard, Paris, 1895.

1239. A. L. Ludington [1988], Length of the 7-number game, Fibonacci Quart.

26, 195–204. 1240. A. Ludington-Young [1990], Length of the n-number game, Fibonacci

Quart. 28, 259–265. 1241. W. F. Lunnon [1986], The Reve’s puzzle, Comput. J. 29, 478. 1242. M. Maamoun and H. Meyniel [1987], On a game of policemen and robber,

Discrete Appl. Math. 17, 307–309. 1243. P. A. MacMahon [1921], New Mathematical Pastimes, Cambridge Uni-

versity Press, Cambridge. 1244. F. Maffray [1986], On kernels in i-triangulated graphs, Discrete Math. 61,

247–251. 1245. F. Maffray [1992], Kernels in perfect line-graphs, J. Combin. Theory

(Ser. B) 55, 1–8. 1246. C. Magnien, H. D. Phan and L. Vuillon [2001], Characterization of lat-

tices induced by (extended) chip firing games, Discrete models: combinatorics, computation, and geometry (Paris, 2001), 229–244 (electronic), Discrete Math. and Theor. Comput. Sci. Proc. pp. 229–244, MR1888776 (2003a:91029).

1247. M. Mamino [2013], On the computational complexity of a game of cops and robbers, Theoret. Comput. Sci. 477, 48–56, 3027882.

http://dx.doi.org/10.1016/j.tcs.2012.11.041

1248. R. Mansfield [1996], Strategies for the Shannon switching game, Amer.

Math. Monthly 103, 250–252. 1249. D. Marcu [1992], On finding a Grundy function, Polytech. Inst. Bucharest

Sci. Bull. Chem. Mater. Sci. 54, 43–47. 1250. G. Martin [1991], Polyominoes: Puzzles and Problems in Tiling, Math.

Assoc. America, Wasington, DC. 1251. G. Martin [2002], Restoring fairness to Dukego, in: More Games of No

Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 79–87, MR1973006 (2004c:91031).

1252. O. Martín-Sánchez and C. Pareja-Flores [2001], Two reflected analyses of

lights out, Math. Mag. 74, 295–304. 1253. F. Mäser [2002], Global threats in combinatorial games: a computa-

tional model with applications to chess endgames, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 137–149, MR1973010 (2004b:91049).

1254. A. Mateescu, G. Păun, G. Rozenberg and A. Salomaa [1995], Parikh prime words and GO-like territories, J.UCS 1(12), 790–810 (electronic), 1392430 (97b:68113).

1255. A. Máthé [2007], The angel of power 2 wins, Combin. Probab. Comput.

16, 363–374, MR2312432 (2008a:91038). 1256. J. G. Mauldon [1978], Num, a variant of nim with no first player win,

Amer. Math. Monthly 85, 575–578. 1257. R. McConville [1974], The History of Board Games, Creative Publica-

tions, Palo Alto, CA. 1258. S. K. McCurdy and R. Nowakowski [2005], Cutthroat, an all-small game

on graphs, Integers, Electr. J of Combinat. Number Theory 5(2), #A13, 13 pp., MR2192091 (2006g:05076).

http://www.integers-ejcnt.org/vol5(2).html

1259. D. P. McIntyre [1942], A new system for playing the game of nim, Amer.

Math. Monthly 49, 44–46. 1260. N. A. McKay [2011], Canonical forms of uptimals, Theoret. Comput. Sci.

412(52), 7122–7132, 2895141.

http://dx.doi.org/10.1016/j.tcs.2011.09.021

1261. N. A. McKay, R. J. Nowakowski and A. A. Siegel [2010], The gods play maze, in: Recreational Mathematics Colloquium I , Assoc. Ludus, Lisbon, pp. 153–159, 2807403.

1262. R. McNaughton [1993], Infinite games played on finite graphs, Ann. Pure

Appl. Logic 65, 149–184. 1263. J. W. A. McWorter [1981], Kriegspiel Hex, Math. Mag. 54, 85–86, solution

to Problem 1084 posed by the author in Math. Mag. 52 (1979) 317. 1264. E. Mead, A. Rosa and C. Huang [1974], The game of SIM: A winning

strategy for the second player, Math. Mag. 47, 243–247. 1265. N. Megiddo, S. L. Hakimi, M. R. Garey, D. S. Johnson and C. H. Pa-

padimitriou [1988], The complexity of searching a graph, J. Assoc. Comput. Mach. 35, 18–44.

1266. K. Mehlhorn, S. Näher and M. Rauch [1990], On the complexity of a game related to the dictionary problem, SIAM J. Comput. 19, 902–906, earlier draft appeared in Proc. 30th Ann. Symp. Foundations of Computer Science, pp. 546–548.

1267. A. Mehrabian [2011], Lower bounds for the cop number when the robber is fast, Combin. Probab. Comput. 20(4), 617–621, 2805400 (2012e:05253).

http://dx.doi.org/10.1017/S0963548311000101

1268. A. Mehrabian [2011], The capture time of grids, Discrete Math. 311(1), 102–105, 2737974 (2011i:05154).

http://dx.doi.org/10.1016/j.disc.2010.10.002

1269. N. Mehta and Á. Seress [2011], Connected, bounded degree, triangle

avoidance games, Electron. J. Combin. 18(1), Paper 193, 37, 2836828. 1270. N. S. Mendelsohn [1946], A psychological game, Amer. Math. Monthly

53, 86–88. 1271. E. Mendelson [2004], Introducing game theory and its applications,

Discrete Mathematics and its Applications (Boca Raton), Chapman & Hall/CRC, Boca Raton, FL, (Ch. 1 is on combinatorial games),

MR2073442 (2005b:91003). 1272. C. G. Méndez [1981], On the law of large numbers, infinite games and

category, Amer. Math. Monthly 88, 40–42. 1273. K. Meng, C. Lin, W. A. Liu and Y. Yang [2011], Q-ary Rényi-Ulam

pathological liar game with one lie, Discrete Appl. Math. 159(6), 478– 483, 2765437 (2012c:91063).

http://dx.doi.org/10.1016/j.dam.2010.12.021

1274. C. Merino [2001], The chip firing game and matroid complexes, Discrete models: combinatorics, computation, and geometry (Paris, 2001) (electronic), Discrete Math. and Theor. Comput. Sci. Proc. pp. 245–255, MR1888777 (2002k:91048).

1275. C. Merino [2005], The chip-firing game, Discrete Math. 302(1-3), 188– 210, 2179643 (2007c:91036).

http://dx.doi.org/10.1016/j.disc.2004.07.033

1276. C. Merino López [1997], Chip firing and the Tutte polynomial, Ann. Comb. 1, 253–259, (C. Merino López = C.M. López = C. Merino is the same author), MR1630779 (99k:90232).

1277. G. A. Mesdal III [2009], Partizan splittles, in: Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 447–461.

1278. G. A. Mesdal and P. Ottaway [2007], Simplification of partizan games in misère play, Integers, Electr. J of Combinat. Number Theory 7, #G06, 12 pp.), (G. A. Mesdal designates the following authors: M. Allen, J. P. Grossman, A. Hill, N. A. McKay, R. J. Nowakowski, T. Plambeck, A. A. Siegel, D. Wolfe, who participated at the 2006 “Games-at-Dal 4” (Dalhousie) conference), MR2299812 (2007k:91054).

http://www.integers-ejcnt.org/vol7.html

1279. D. Mey [1994], Finite games for a predicate logic without contractions,

Theoret. Comput. Sci. 123, 341–349. 1280. F. Meyer auf der Heide [1981], A comparison of two variations of a pebble

game on graphs, Theoret. Comput. Sci. 13, 315–322. 1281. H. Meyniel and J.-P. Roudneff [1988], The vertex picking game and a

variation of the game of dots and boxes, Discrete Math. 70, 311–313, MR0955128 (89f:05111).

1282. P. Micek and B. Walczak [2011], A graph-grabbing game, Combin. Probab. Comput. 20(4), 623–629, 2805401 (2012d:05252).

http://dx.doi.org/10.1017/S0963548311000071

1283. P. Micek and B. Walczak [2012], Parity in graph sharing games, Discrete

Math. 312, 1788–1795. 1284. D. Michie and I. Bratko [1987], Ideas on knowledge synthesis stemming

from the KBBKN endgame, Internat. Comp. Chess Assoc. J. 10, 3–13. 1285. R. Milley, R. J. Nowakowski and P. Ottaway [2012], Misère moniod of

one-handed alternating games, Integers 12B, A1, 12, in Proceedings of

the Integers Conference 2011. 1286. J. Milnor [1953], Sums of positional games, Ann. of Math. Stud. (Contri-

butions to the Theory of Games, H. W. Kuhn and A. W. Tucker, eds.), Princeton 2(28), 291–301.

1287. P. Min Lin [1982], Principal partition of graphs and connectivity games,

J. Franklin Inst. 314, 203–210. 1288. S. Minsker [1989], The towers of Hanoi rainbow problem: coloring the

rings, J. Algorithms 10, 1–19. 1289. S. Minsker [1991], The towers of Antwerpen problem, Inform. Process.

Lett. 38, 107–111. 1290. J. Missigman and R. Weida [2001], An easy solution to mini lights out,

Math. Mag. 74, 57–59. 1291. D. Moews [1991], Sums of games born on days 2 and 3, Theoret. Comput.

Sci. (Math Games) 91, 119–128, MR1142561 (93b:90130). 1292. D. Moews [1992], Pebbling graphs, J. Combin. Theory (Ser. B) 55, 244–

252. 1293. D. Moews [1996], Coin-sliding and Go, Theoret. Comput. Sci. (Math

Games) 164, 253–276. 1294. D. Moews [1996], Infinitesimals and coin-sliding, in: Games of No Chance,

Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 315–327.

1295. D. Moews [1996], Loopy games and Go, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 259–272, MR1427968 (98d:90152).

1296. D. Moews [2002], The abstract structure of the group of games, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 49–57, MR1973004 (2004b:91034).

1297. M. Montassier, A. Pêcher, A. Raspaud, D. B. West and X. Zhu [2010], Decomposition of sparse graphs, with application to game coloring number, Discrete Math. 310(10-11), 1520–1523, 2601259 (2011g:05244).

http://dx.doi.org/10.1016/j.disc.2010.01.008

1298. C. Moore and D. Eppstein [2002], 1-dimensional peg solitaire, and duotaire, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 341–350, MR1973022.

1299. E. H. Moore [1909–1910], A generalization of the game called nim, Ann.

of Math. (Ser. 2) 11, 93–94. 1300. A. H. Moorehead and G. Mott-Smith [1963], Hoyle’s Rules of Games,

Signet, New American Library.

1301. F. L. Morris [1981], Playing disjunctive sums is polynomial space com-

plete, Internat. J. Game Theory 10, 195–205. 1302. D. R. Morrison [1980], A Stolarsky array of Wythoff pairs, in: A collection

of manuscripts related to the Fibonacci sequence, Fibonacci Assoc., Santa Clara, Calif., pp. 134–136, MR624110 (82j:05030).

1303. R. E. Morrison, E. J. Friedman and A. S. Landsberg [2011], Combinatorial games with a pass: A dynamical systems approach, Chaos 21, 043108 (2011); doi:10.1063/1.3650234 21.

1304. M. Morse and G. A. Hedlund [1944], Unending chess, symbolic dynamics

and a problem in semigroups, Duke Math. J. 11, 1–7. 1305. M. Müller [2003], Conditional combinatorial games and their application

to analyzing capturing races in Go, Information Sciences 154, 189–202. 1306. M. Müller and R. Gasser [1996], Conditional combinatorial games and

their application to analyzing capturing races in Go, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 273–284.

1307. M. Müller and T. Tegos [2002], Experiments in computer Amazons, in: More games of no chance (Berkeley, CA, 2000), Vol. 42 of Math. Sci. Res. Inst. Publ., Cambridge Univ. Press, Cambridge, pp. 243–260, MR1973016 (2004b:91050).

1308. D. J. Mundfrom [1994], A problem in permutations: the game of ‘Mousetrap’, European J. Combin. 15(6), 555–560, 1302079 (95m:05015).

http://dx.doi.org/10.1006/eujc.1994.1057

1309. D. Mundici [1991], Logic and algebra in Ulam’s searching game with lies,

Jbuch. Kurt-Gödel-Ges. pp. 109–114 (1993), MR1213606 (94j:03130). 1310. D. Mundici [1992], The logic of Ulam’s game with lies, in: Knowledge,

Belief, and Strategic Interaction (Castiglioncello, 1989), Cambridge Stud. Probab. Induc. Decis. Theory, Cambridge Univ. Press, Cambridge, pp. 275–284, MR1206717 (94c:90133).

1311. D. Mundici and T. Trombetta [1997], Optimal comparison strategies in Ulam’s searching game with two errors, Theoret. Comput. Sci. (Math Games) 182, 217–232.

1312. H. J. R. Murray [1952], A History of Board Games Other Than Chess,

Oxford University Press. 1313. T. Mütze and R. Spöhel [2011], On the path-avoidance vertex-coloring

game, Electron. J. Combin. 18(1), Paper 163, 33, 2831099. 1314. B. Nadel [1990], Representation selection for constraint satisfaction: a

case study using n-queens, IEEE Expert 5 issue 3, 16–23. 1315. H. Nagamochi [2011], Cop-robber guarding game with cycle robber-

region, Theoret. Comput. Sci. 412(4-5), 383–390, 2778471 (2012b:05181).

http://dx.doi.org/10.1016/j.tcs.2010.04.014

1316. T. Nakamura [2009], On counting liberties in capturing races of Go, in: Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 177–196.

1317. T. Nakamura [2013], Evaluating Territories of Go Positions with Capturing Races, in: Games of No Chance 4 , Cambridge University Press, to appear.

1318. T. Nakamura and E. Berlekamp [2003], Analysis of composite corridors, Proc. Intern. Conference on Computers and Games CG’2002, Edmonton, Alberta, Canada, July 2002, (Y. Björnsson, M. Müller and J. Schaeffer, eds.), Vol. LNCS 288, Lecture Notes in Computer Science, Springer, pp. 213–229.

1319. B. Nalebuff [1989], The other person’s envelope is always greener, J. Eco-

nomic Perspectives 3 issue 1, 171–181. 1320. A. Napier [1970], A new game in town, Empire Mag., Denver Post, May

2. 1321. Z. Nedev [2008], Universal sets and the vector game, Integers 8, A45, 5,

2472063 (2010b:91053). 1322. Z. Nedev [2010], An O(n)-round strategy for the Magnus-Derek game,

Algorithms (Basel) 3(3), 244–254, 2725450.

http://dx.doi.org/10.3390/a3030244

1323. Z. Nedev and S. Muthukrishnan [2008], The Magnus-Derek game, Theoret. Comput. Sci. 393(1-3), 124–132, 2397246 (2009h:91052).

http://dx.doi.org/10.1016/j.tcs.2007.11.016

1324. Z. Nedev and A. Quas [2008], Balanced sets and the vector game, Int. J.

Number Theory 4, 339–347, MR2424326. 1325. A. Negro and M. Sereno [1992], Solution of Ulam’s problem on binary

search with three lies, J. Combin. Theory Ser. A 59, 149–154, MR1141331 (92h:05013).

1326. A. Negro and M. Sereno [1992], Ulam’s searching game with three lies,

Adv. in Appl. Math. 13, 404–428, MR1190120 (93i:90129). 1327. J. Nešetřil and E. Sopena [2001], On the oriented game chromatic number,

Electr. J. Combin. 8(2), #R14, 13 pp., Volume in honor of Aviezri S. Fraenkel, MR1853265 (2002h:05069).

http://www.combinatorics.org/

1328. J. Nešetřil and R. Thomas [1987], Well quasi-orderings, long games and a combinatorial study of undecidability, in: Logic and combinatorics (Arcata, Calif., 1985), Vol. 65 of Contemp. Math., Amer. Math. Soc., Providence, RI, pp. 281–293, 891254 (88i:03098).

http://dx.doi.org/10.1090/conm/065/891254

1329. S. Neufeld and R. J. Nowakowski [1993], A vertex-to-vertex pursuit game played with disjoint sets of edges, in: Finite and Infinite Combinatorics in Sets and Logic (N. W. Sauer et al., eds.), Kluwer, Dordrecht, pp. 299–312.

1330. S. Neufeld and R. J. Nowakowski [1998], A game of cops and robbers played on products of graphs, Discrete Math. 186, 253–268.

1331. J. Nievergelt, F. Maeser, B. Mann, K. Roeseler, M. Schulze and C. Wirth [1999], CRASH! Mathematik und kombinatorisches Chaos prallen aufeinander, Informatik Spektrum 22, 45–48, (German).

1332. G. Nivasch [2006], The Sprague-Grundy function of the game Euclid,

Discrete Math. 306(21), 2798–2800, MR2264378 (2007i:91039). 1333. G. Nivasch [2009], More on the Sprague-Grundy function for Wythoff’s

game, in: Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 377–410.

1334. I. Niven [1988], Coding theory applied to a problem of Ulam, Math. Mag.

61, 275–281. 1335. H. Noon and G. V. Brummelen [2006], The non-attacking queens game,

College Math. J. 37, 223–227. 1336. R. J. Nowakowski [1991], …, Welter’s game, Sylver coinage, dots-and-

boxes, …, in: Combinatorial Games, Proc. Symp. Appl. Math. (R. K. Guy, ed.), Vol. 43, Amer. Math. Soc., Providence, RI, pp. 155–182.

1337. R. J. Nowakowski and P. Ottaway [2005], Vertex Deletion Games with Parity Rules, Integers, Electr. J of Combinat. Number Theory 5(2), #A15, 16 pp., MR2192093.

http://www.integers-ejcnt.org/vol5(2).html

1338. R. J. Nowakowski and P. Ottaway [2011], Option-closed games, Contrib.

Discrete Math. 6(1), 142–153, 2800733 (2012e:91080). 1339. R. J. Nowakowski and D. G. Poole [1996], Geography played on prod-

ucts of directed cycles, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 329–337.

1340. R. J. Nowakowski and A. A. Siegel [2007], Partizan geography on K_{n}×K_{2}, de Gruyter, pp. 389–401, Proc. Integers Conference, Carrollton, Georgia, October 27-30,2005, in celebration of the 70th birthday of Ronald Graham. B. Landman, M. Nathanson, J. Nešetřil, R. Nowakowski, C. Pomerance eds., appeared also in Integers, Electr. J. of Combinat. Number Theory 7(20), special volume in honor of Ron Graham, #A29, 14 pp., MR2337063.

http://www.integers-ejcnt.org/vol7(2).html

1341. R. Nowakowski and P. Winkler [1983], Vertex-to-vertex pursuit in a graph,

Discrete Math. 43, 235–239. 1342. S. P. Nudelman [1995], The modular n-queens problem in higher dimen-

sions, Discrete Math. 146, 159–167. 1343. T. H. O’Beirne [1984], Puzzles and Paradoxes, Dover, New York, NY.

(Appeared previously by Oxford University Press, London, 1965.). 1344. G. L. O’Brian [1978-79], The graph of positions in the game of SIM, J.

Recr. Math. 11, 3–9.

1345. J. Olson [1985], A balancing strategy, J. Combin. Theory Ser. A 40, 175–

178. 1346. T. Ooya and J. Akiyama [2003], Impact of binary and Fibonacci expan-

sions of numbers on winning strategies for Nim-like games, Internat. J. Math. Ed. Sci. Tech. 34, 121–128, MR1958736.

1347. H. K. Orman [1996], Pentominoes: a first player win, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 339–344.

1348. P. R. J. Östergård and W. D. Weakley [2001], Values of domination numbers of the queen’s graph, Electr. J. Combin. 8(1), #R29, 19 pp.

http://www.combinatorics.org/

1349. J. Pach [1992], On the game of Misery, Studia Sci. Math. Hungar. 27,

355–360. 1350. E. W. Packel [1987], The algorithm designer versus nature: a game-theore-

tic approach to information-based complexity, J. Complexity 3, 244–257. 1351. C. H. Papadimitriou [1985], Games against nature, J. Comput. System

Sci. 31, 288–301. 1352. C. H. Papadimitriou [1994], Computational Complexity, Addison-Wesley,

Chapter 19: Polynomial Space. 1353. C. H. Papadimitriou [1994], On the complexity of the parity argument

and other inefficient proofs of existence, J. Comput. System Sci. 48(3), 498–532, 31st Annual Symposium on Foundations of Computer Science (FOCS) (St. Louis, MO, 1990), 1279412 (95j:68061).

http://dx.doi.org/10.1016/S0022-0000(05)80063-7

1354. C. H. Papadimitriou, P. Raghavan, M. Sudan and H. Tamaki [1994], Motion planning on a graph (extended abstract), Proc. 35-th Annual IEEE Symp. on Foundations of Computer Science, Santa Fe, NM, pp. 511–520.

1355. A. Papaioannou [1982], A Hamiltonian game, Ann. Discrete Math. 13,

171–178. 1356. T. Pappas [1994], The Magic of Mathematics, Wide World, San Carlos. 1357. I. Parberry [1997], An efficient algorithm for the knight’s tour problem,

Discrete Appl. Math. 73(3), 251–260, 1438157 (98b:05066).

http://dx.doi.org/10.1016/S0166-218X(96)00010-8

1358. D. Parlett [1999], The Oxford History of Board Games, Oxford University

Press. 1359. T. D. Parsons [1978], Pursuit-evasion in a graph, in: Theory and Appli-

cations of Graphs (Y. Alavi and D. R. Lick, eds.), Springer-Verlag, pp. 426–441.

1360. T. D. Parsons [1978], The search number of a connected graph, Proc. 9th South-Eastern Conf. on Combinatorics, Graph Theory, and Computing,, pp. 549–554.

1361. O. Patashnik [1980], Qubic: 4 × 4 × 4 Tic-Tac-Toe, Math. Mag. 53, 202– 1362. M. B. Paterson and D. R. Stinson [2010], Yet another hat game, Electron.

J. Combin. 17(1), Research Paper 86, 12, 2661389 (2011e:91055).

http://www.combinatorics.org/Volume_17/Abstracts/v17i1r86.
html

1363. J. L. Paul [1978], Tic-Tac-Toe in n dimensions, Math. Mag. 51, 45–49. 1364. W. J. Paul, E. J. Prauss and R. Reischuk [1980], On alternation, Acta

Informatica 14, 243–255. 1365. W. J. Paul and R. Reischuk [1980], On alternation, II, Acta Informatica

14, 391–403. 1366. W. J. Paul, R. E. Tarjan and J. R. Celoni [1976/77], Space bounds for

a game on graphs, Math. Systems Theory 10, 239–251, correction ibid. 11 (1977/78), 85. First appeared in Eighth Annual ACM Symposium on Theory of Computing (Hershey, Pa., 1976), Assoc. Comput. Mach., New York, NY, 1976, pp 149–160.

1367. M. M. Paulhus [1999], Beggar my neighbour, Amer. Math. Monthly 106,

162–165. 1368. S. Payne and E. Robeva [2013], Artificial Intelligence for Bidding Hex,

in: Games of No Chance 4 , Cambridge University Press, to appear. 1369. J. Pearl [1980], Asymptotic properties of minimax trees and game-sear-

ching procedures, Artificial Intelligence 14, 113–138. 1370. J. Pearl [1984], Heuristics: Intelligent Search Strategies for Computer

Problem Solving, Addison-Wesley, Reading, MA. 1371. A. Pedrotti [2002], Playing by searching: two strategies against a linearly

bounded liar, Theoret. Comput. Sci. 282, 285–302, special ”Fun With Algorithms” issue, MR1909053 (2003m:91010).

1372. A. Pekeč [1996], A winning strategy for the Ramsey graph game, Combin.

Probab. Comput. 5, 267–276. 1373. A. Pelc [1986], Lie patterns in search procedures, Theoret. Comput. Sci.

47, 61–69, MR871464 (88b:68020). 1374. A. Pelc [1987], Solution of Ulam’s problem on searching with a lie, J.

Combin. Theory (Ser. A) 44, 129–140. 1375. A. Pelc [1988], Prefix search with a lie, J. Combin. Theory (Ser. A) 48,

165–173. 1376. A. Pelc [1989], Detecting errors in searching games, J. Combin. Theory

Ser. A 51(1), 43–54, 993647 (90e:90152).

http://dx.doi.org/10.1016/0097-3165(89)90075-7

1377. A. Pelc [2002], Searching games with errors—fifty years of coping with liars, Theoret. Comput. Sci. (Math Games) 270, 71–109, MR1871067 (2002h:68040).

1378. D. H. Pelletier [1987], Merlin’s magic square, Amer. Math. Monthly 94,

143–150. 1379. H. Peng and C. H. Yan [1998], Balancing game with a buffer, Adv. in

Appl. Math. 21, 193–204.

1380. Y. Peres, O. Schramm, S. Sheffield and D. B. Wilson [2007], Random-turn

Hex and other selection games, Amer. Math. Monthly 114, 373–387. 1381. G. L. Peterson [1979], Press-Ups is Pspace-complete, Dept. of Computer

Science, The University of Rochester, Rochester New York, 14627, unpublished manuscript.

1382. G. L. Peterson and J. H. Reif [1979], Multiple-person alternation, Proc. 20th Ann. Symp. Foundations Computer Science (San Juan, Puerto Rico, Oct. 1979), IEEE Computer Soc., Long Beach, CA, pp. 348–363.

1383. M. Petković [1997], Mathematics and chess, Dover Publications Inc., Mi-

neola, NY, 110 entertaining problems and solutions, 1474728 (98j:00003). 1384. C. Pickover [2002], The fractal society, in: Puzzler’s Tribute: a Feast

for the Mind, pp. 377–381, honoring Martin Gardner (D. Wolfe and T. Rodgers, eds.), A K Peters, Natick, MA.

1385. O. Pikhurko [2003], Breaking symmetry on complete bipartite graphs of odd size, Integers, Electr. J. of Combinat. Number Theory 3, #G4, 9 pp., Comb. Games Sect., MR2036488 (2004k:05117).

http://www.integers-ejcnt.org/vol3.html

1386. N. Pippenger [1980], Pebbling, Proc. 5th IBM Symp. Math. Foundations

of Computer Science, IBM, Japan, 19 pp. 1387. N. Pippenger [1982], Advances in pebbling, Proc. 9th Internat. Colloq.

Automata, Languages and Programming, Lecture Notes in Computer Science (M. Nielson and E. M. Schmidt, eds.), Vol. 140, Springer Verlag, New York, NY, pp. 407–417.

1388. T. E. Plambeck [1992], Daisies, Kayles, and the Sibert–Conway decomposition in misère octal games, Theoret. Comput. Sci. (Math Games) 96, 361–388, MR1160551 (93c:90108).

1389. T. E. Plambeck [2005], Taming the wild in impartial combinatorial games, Integers, Electr. J. of Combinat. Number Theory 5, #G5(1), 36 pp., Comb. Games Sect., MR2192253 (2006g:91044).

http://www.integers-ejcnt.org/vol5.html

1390. T. Plambeck [2009], Advances in losing, in: Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 57–89.

1391. T. E. Plambeck [2009], Misere play of G-A-R-D-N-R, the G4G7 heptagon game, in: Mathematical Wizardry for a Gardner, Volume honoring Martin Gardner, A K Peters, Natick, MA, pp. 107–113, E. Pegg Jr, A. H. Schoen, and T. Rodgers, eds.

1392. T. E. Plambeck and A. N. Siegel [2008], Misère quotients for impartial

games, J. Combin. Theory Ser. A 115, 593–622, 2407915 (2009m:91036). 1393. V. Pless [1991], Games and codes, in: Combinatorial Games, Proc. Symp.

Appl. Math. (R. K. Guy, ed.), Vol. 43, Amer. Math. Soc., Providence, RI, pp. 101–110.

1394. A. Pluhár [2002], The accelerated k-in-a-row game, Theoret. Comput. Sci.

(Math Games) 270, 865–875, MR1871100 (2002i:05017). 1395. R. Polizzi and F. Schaefer [1991], Spin Again, Chronicle Books. 1396. G. Pólya [1921], Über die “doppelt-periodischen” Lösungen des n-Damen-

Problems, in: W. Ahrens, Mathematische Unterhaltungen und Spiele, Vol. 1, B.G. Teubner, Leipzig, 1918, pp. 364–374, also appeared in vol. IV of Pólya’s Collected Works, MIT Press, Cambridge, London, 1984 (G.-C Rota ed.), pp. 237-247.

1397. D. Poole [1992], The bottleneck towers of Hanoi problem, J. Recr. Math.

24, 203–207. 1398. D. G. Poole [1994], The towers and triangles of Professor Claus (or, Pascal

knows Hanoi), Math. Mag. 67, 323–344. 1399. P. Prałat [2010], When does a random graph have constant cop number?,

Australas. J. Combin. 46, 285–296, 2598712 (2011f:05291). 1400. O. Pretzel [2002], Characterization of simple edge-firing games, Inform.

Process. Lett. 84, 235–236, MR1931725 (2003i:05128). 1401. D. Pritchard [1994], The Family Book of Games, Sceptre Books, Time-

Life Books, Brockhampton Press. 1402. J. Propp [1994], A new take-away game, in: The Lighter Side of Mathe-

matics, Proc. E. Strens Memorial Conf. on Recr. Math. and its History, Calgary, 1986, Spectrum Series (R. K. Guy and R. E. Woodrow, eds.), Math. Assoc. of America, Washington, DC, pp. 212–221.

1403. J. Propp [1994], Further ant-ics, Math. Intelligencer 16, 37–42, 1251666 (94m:05020).

http://dx.doi.org/10.1007/BF03026614

1404. J. Propp [1996], About David Richman (Prologue to the paper by J. D. Lazarus et al.), in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, p. 437.

1405. J. Propp [2000], Three-player impartial games, Theoret. Comput. Sci.

(Math Games) 233, 263–278, MR1732189 (2001i:91040). 1406. J. Propp and D. Ullman [1992], On the cookie game, Internat. J. Game

Theory 20, 313–324, MR1163932 (93b:90131). 1407. P. Pudlák and J. Sgall [1997], An upper bound for a communication game

related to time-space tradeoffs, in: The Mathematics of Paul Erdős (R. L. Graham and J. Nešetřil, eds.), Vol. I, Springer, Berlin, pp. 393–399.

1408. A. Pultr and F. L. Morris [1984], Prohibiting repetitions makes playing games substantially harder, Internat. J. Game Theory 13(1), 27–40, 741584 (86i:90133).

http://dx.doi.org/10.1007/BF01769863

1409. A. Pultr and J. Úlehla [1985], Remarks on strategies in combinatorial games, Discrete Appl. Math. 12(2), 165–173, 808457 (87c:90243).

http://dx.doi.org/10.1016/0166-218X(85)90070-8

1410. Y. Qing and J. J. Watkins [2006], Knight’s tours for cubes and boxes, Proceedings of the Thirty-Seventh Southeastern International Conference on Combinatorics, Graph Theory and Computing, Vol. 181, pp. 41–48, 2311267 (2007m:05148).

1411. A. Quilliot [1983], Discrete pursuit games, Congr. Numer. 38, 227–241, Proc. 13th Southeastern Conf. on Combinatorics, Graph Theory and Computing, Boca Raton, FL, 1982.

1412. A. Quilliot [1985], A short note about pursuit games played on a graph with a given genus, J. Combin. Theory Ser. B 38(1), 89–92, 782627 (86g:05088).

http://dx.doi.org/10.1016/0095-8956(85)90093-0

1413. A. Quilliot [1986], Some results about pursuit games on metric spaces obtained through graph theory techniques, European J. Combin. 7(1), 55–66, 850144 (87i:90381).

1414. M. O. Rabin [1957], Effective computability of winning strategies, Ann. of Math. Stud. (Contributions to the Theory of Games), Princeton 3(39), 147–157.

1415. M. O. Rabin [1976], Probabilistic algorithms, Proc. Symp. on New Directions and Recent Results in Algorithms and Complexity (J. F. Traub, ed.), Carnegie-Mellon, Academic Press, New York, NY, pp. 21–39.

1416. I. Rajasingh, B. Rajan and J. Punitha [2007], Kernel in cycle related

graphs, Int. J. Math. Comput. Sci. 2, 147–153, 2345016 (2008g:05086). 1417. P. Manuel, I. Rajasingh, B. Rajan and J. Punitha [2009], Kernel in ori-

ented circulant graphs, in: Combinatorial algorithms, Vol. 5874 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 396–407, 2577955.

1418. D. Ratner and M. Warmuth [1990], The (n^{2} − 1)-puzzle and related relo-

cation problems, J. Symbolic Comput. 10, 111–137. 1419. B. Ravikumar [2004], Peg-solitaire, string rewriting systems and finite au-

tomata, Theoret. Comput. Sci. 321, 383–394, Appeared first under same title in Proc. 8th Internat. Symp. Algorithms and Computation, Singapore, 233-242, 1997, MR 2005e:68119, MR2076153 (2005e:68119).

1420. B. Ravikumar and K. B. Lakshmanan [1982], Coping with known patterns of lies in a search game, in: Foundations of software technology and theoretical computer science (Bangalore, 1982), Nat. Centre Software Develop. Comput. Tech., Bombay, pp. 363–377, MR678245 (83m:68114).

1421. B. Ravikumar and K. B. Lakshmanan [1984], Coping with known patterns

of lies in a search game, Theoret. Comput. Sci. 33, 85–94. 1422. J. W. S. Rayleigh [1937], The Theory of Sound, MacMillan, London, 1st

ed. 1877, 2nd ed. 1894, reprinted 1928,1929,1937. There is also a Dover 1945 publication, which is a reprint of the 2nd. The “sound” equivalent of Beatty’s theorem, is stated, without proof, in sect. 92a, pp. 122-123, in the 1937 reprint of the 2nd ed., the only one I saw. Kevin O’Bryant told me that he checked the 1st edition and the statement is not there, MR0016009 (7,500e).

1423. N. Reading [1999], Nim-regularity of graphs, Electr. J. Combinatorics 6, #R11, 8 pp.

http://www.combinatorics.org/

1424. M. Reichling [1987], A simplified solution of the N queens’ problem, In-

form. Process. Lett. 25, 253–255. 1425. J. H. Reif [1984], The complexity of two-player games of incomplete infor-

mation, J. Comput. System Sci. 29, 274–301, earlier draft entitled Universal games of incomplete information, appeared in Proc. 11th Ann. ACM Symp. Theory of Computing (Atlanta, GA, 1979), Assoc. Comput. Mach., New York, NY, pp. 288–308.

1426. S. Reisch [1980], Gobang ist PSPACE-vollständig, Acta Informatica 13,

59–66. 1427. S. Reisch [1981], Hex ist PSPACE-vollständig, Acta Informatica 15, 167–

191. 1428. M. Reiss [1857], Beiträge zur Theorie des Solitär-Spiels, Crelles Journal

54, 344–379. 1429. P. Rendell [2001], Turing universality of the game of life, in: Collision-

Based Computing, Springer Verlag, London, UK, pp. 513 – 539. 1430. C. S. ReVelle and K. E. Rosing [2000], Defendens imperium romanum

[Defending the Roman Empire]: a classical problem in military strategy, Amer. Math. Monthly 107, 585–594.

1431. M. Richardson [1953], Extension theorems for solutions of irreflexive re-

lations, Proc. Nat. Acad. Sci. USA 39, 649. 1432. M. Richardson [1953], Solutions of irreflexive relations, Ann. of Math. 58,

573–590. 1433. R. D. Ringeisen [1974], Isolation, a game on a graph, Math. Mag. 47,

132–138. 1434. R. L. Rivest, A. R. Meyer, D. J. Kleitman, K. Winklman and J. Spencer

[1980], Coping with errors in binary search procedures, J. Comput. System Sci. 20, 396–404.

1435. I. Rivin, I. Vardi and P. Zimmermann [1994], The n-queens problem,

Amer. Math. Monthly 101, 629–639. 1436. I. Rivin and R. Zabih [1992], A dynamic programming solution to the

N-queens problem, Inform. Process. Lett. 41, 253–256. 1437. E. Robertson and I. Munro [1978], NP-completeness, puzzles and games,

Utilitas Math. 13, 99–116. 1438. A. G. Robinson and A. J. Goldman [1989], The set coincidence game:

complexity, attainability, and symmetric strategies, J. Comput. System Sci. 39, 376–387.

1439. A. G. Robinson and A. J. Goldman [1990], On Ringeisen’s isolation game,

Discrete Math. 80, 297–312. 1440. A. G. Robinson and A. J. Goldman [1990], On the set coincidence game,

Discrete Math. 84, 261–283. 1441. A. G. Robinson and A. J. Goldman [1991], On Ringeisen’s isolation game,

II, Discrete Math. 90, 153–167.

1442. A. G. Robinson and A. J. Goldman [1993], The isolation game for regular

graphs, Discrete Math. 112, 173–184. 1443. J. M. Robson [1983], The complexity of Go, Proc. Information Processing

83 (R. E. A. Mason, ed.), Elsevier, Amsterdam, pp. 413–417. 1444. J. M. Robson [1984], Combinatorial games with exponential space com-

plete decision problems, in: Mathematical foundations of computer science, 1984 (Prague, 1984), Vol. 176 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 498–506, 783481.

http://dx.doi.org/10.1007/BFb0030333

1445. J. M. Robson [1984], N by N checkers is Exptime complete, SIAM J.

Comput. 13, 252–267. 1446. J. M. Robson [1985], Alternation with restrictions on looping, Inform.

and Control 67, 2–11. 1447. E. Y. Rodin [1989], A pursuit-evasion bibliography – version 2, Comput.

Math. Appl. 18, 245–320. 1448. J. S. Rohl [1983], A faster lexicographical n-queens algorithm, Inform.

Process. Lett. 17, 231–233. 1449. J. S. Rohl and T. D. Gedeon [1986], The Reve’s puzzle, Comput. J. 29,

187–188, Corrigendum, Ibid. 31 (1988), 190. 1450. I. Roizen and J. Pearl [1983], A minimax algorithm better than alpha-

beta? Yes and no, Artificial Intelligence 21, 199–220. 1451. I. Rosenholtz [1993], Solving some variations on a variant of Tic-Tac-Toe

using invariant subsets, J. Recr. Math. 25, 128–135. 1452. A. S. C. Ross [1953], The name of the game of Nim, Note 2334, Math.

Gaz. 37, 119–120. 1453. A. E. Roth [1978], A note concerning asymmetric games on graphs, Naval

Res. Logistics 25, 365–367. 1454. A. E. Roth [1978], Two-person games on graphs, J. Combin. Theory Ser.

B 24(2), 238–241, 486149 (80c:90159).

http://dx.doi.org/10.1016/0095-8956(78)90026-6

1455. T. Roth [1974], The tower of Brahma revisited, J. Recr. Math. 7, 116–119. 1456. E. M. Rounds and S. S. Yau [1974], A winning strategy for SIM, J. Recr.

Math. 7, 193–202. 1457. W. L. Ruzzo [1980], Tree-size bounded alternation, J. Comput. Systems

Sci. 21, 218–235. 1458. S. Sackson [1969], A Gamut of Games, Random House. 1459. I. Safro and L. Segel [2003], Collective stochastic versions of playable

games as metaphors for complex biosystems: team Connect Four, Complexity 8 issue 5, 46–55, MR2018947.

1460. M. Saks and A. Wigderson [1986], Probabilistic Boolean decision trees and the complexity of evaluating game trees, Proc. 27th Ann. Symp. Foundations of Computer Science (Toronto, Ont., Canada), IEEE Computer Soc., Washington, DC, pp. 29–38.

1461. D. Samet, I. Samet and D. Schmeidler [2004], One observation behind two-envelope puzzles, Amer. Math. Monthly 111, 347–351, MR2057189 (2005e:00005).

1462. C. P. dos Santos [2011], Embedding processes in combinatorial game theory, Discrete Appl. Math. 159(8), 675–682, 2782625 (2012d:91054).

http://dx.doi.org/10.1016/j.dam.2010.11.019

1463. C. P. d. Santos and J. N. Silva [2008], Konane has infinite Nim-dimension,

Integers 8, G2, 6, 2393375 (2008k:91052). 1464. A. Sapir [2004], The tower of Hanoi with forbidden moves, Comput. J.

47, 20–24. 1465. U. K. Sarkar [2000], On the design of a constructive algorithm to solve the

multi-peg towers of Hanoi problem, Theoret. Comput. Sci. (Math Games) 237, 407–421, MR1756218 (2001k:05025).

1466. R. Savani and B. von Stengel [2006], Hard-to-solve bimatrix games,

Econometrica 74, 397–429. 1467. M. Sato [1972], Grundy functions and linear games, Publ. Res. Inst. Math.

Sciences, Kyoto Univ. 7, 645–658. 1468. F. Scarioni and H. G. Speranza [1984], A probabilistic analysis of an error-

correcting algorithm for the Towers of Hanoi puzzle, Inform. Process. Lett. 18, 99–103.

1469. W. L. Schaaf [1955, 1970, 1973, 1978], A Bibliography of Recreational Mathematics, Vol. I – IV, Nat’l. Council of Teachers of Mathematics, Reston, VA.

1470. T. J. Schaefer [1976], Complexity of decision problems based on finite twoperson perfect information games, Proc. 8th Ann. ACM Symp. Theory of Computing (Hershey, PA, 1976), Assoc. Comput. Mach., New York, NY, pp. 41–49.

1471. T. J. Schaefer [1978], On the complexity of some two-person perfect-in-

formation games, J. Comput. System Sci. 16, 185–225. 1472. J. Schaeffer, N. Burch, Y. Björnsson, A. Kishimoto, M. Müller, R. Lake,

P. Lu and S. Sutphen [2007], Checkers is solved, Science 317(5844), 1518– 1522, MR2348441.

1473. J. Schaeffer and R. Lake [1996], Solving the game of checkers, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 119–133.

http://www.msri.org/publications/books/Book29/files/
schaeffer.ps.gz

1474. U. Schauz [2009], Mr. Paint and Mrs. Correct, Electron. J. Combin. 16(1), Research Paper 77, 18, 2515754 (2010i:91064).

http://www.combinatorics.org/Volume_16/Abstracts/v16i1r77.
html

1475. U. Schauz [2011], Colorings and nowhere-zero flows of graphs in terms of Berlekamp’s switching game, Electron. J. Combin. 18(1), Paper 65, 33,

2788682 (2012e:05254). 1476. M. Scheepers [1994], Variations on a game of Gale (II): Markov strategies,

Theoret. Comput. Sci. (Math Games) 129, 385–396. 1477. D. Schleicher and M. Stoll [2006], An introduction to Conway’s games and

numbers, Mosc. Math. J. 6(2), 359–388, 407, MR2270619 (2007m:91033). 1478. G. Schmidt and T. Ströhlein [1985], On kernels of graphs and solutions

of games: a synopsis based on relations and fixpoints, SIAM J. Alg. Disc. Math. 6, 54–65.

1479. R. W. Schmittberger [1992], New Rules for Classic Games, Wiley, New

York. 1480. G. Schrage [1985], A two-dimensional generalization of Grundy’s game,

Fibonacci Quart. 23, 325–329. 1481. H. Schubert [1953], Mathematische Mussestunden, De Gruyter, Berlin,

neubearbeitet von F. Fitting, Elfte Auflage. 1482. F. Schuh [1952], Spel van delers (The game of divisors), Nieuw Tijdschrift

voor Wiskunde 39, 299–304. 1483. F. Schuh [1968], The Master Book of Mathematical Recreations, Dover,

New York, NY, translated by F. Göbel, edited by T. H. O’Beirne. 1484. U. Schwalbe and P. Walker [2001], Zermelo and the early history of

game theory, Games Econom. Behav. 34(1), 123–137, With an appendix by Ernst Zermelo, translated from German by the authors, 1895174 (2003a:01019).

http://dx.doi.org/10.1006/game.2000.0794

1485. B. L. Schwartz [1971], Some extensions of Nim, Math. Mag. 44, 252–257. 1486. B. L. Schwartz, ed. [1979], Mathematical solitaires and games, Baywood

Publishing Company, Farmingdale, NY, pp. 37–81. 1487. A. J. Schwenk [1970], Take-away games, Fibonacci Quart. 8, 225–234. 1488. A. J. Schwenk [1991], Which rectangular chessboards have a knight’s

tour?, Math. Mag. 64, 325–332, MR1141559 (93c:05081). 1489. A. J. Schwenk [2000], What is the correct way to seed a knockout tour-

nament?, Amer. Math. Monthly 107, 140–150. 1490. R. S. Scorer, P. M. Grundy and C. A. B. Smith [1944], Some binary

games, Math. Gaz. 280, 96–103. 1491. A. Scott and U. Stege [2008], Parameterized chess, in: Parameterized and

exact computation, Vol. 5018 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 172–189, 2503563 (2010f:68062).

http://dx.doi.org/10.1007/978-3-540-79723-4_17

1492. A. Scott and U. Stege [2010], Parameterized pursuit-evasion games, Theoret. Comput. Sci. 411(43), 3845–3858, 2779755 (2012c:68102).

http://dx.doi.org/10.1016/j.tcs.2010.07.004

1493. S. Seager [2012], Locating a robber on a graph, Discrete Math. 312, 3265–

3269. 1494. M. Sereno [1998], Binary search with errors and variable cost queries,

Inform. Process. Lett. 68, 261–270, MR1664741 (99i:68026).

1495. Á. Seress [1992], On Hajnal’s triangle-free game, Graphs Combin. 8, 75–

79. 1496. Á. Seress and T. Szabó [1999], On Erdös’ Eulerian trail game, Graphs

Combin. 15, 233–237. 1497. J. Sgall [2001], Solution of David Gale’s lion and man problem, Theoret.

Comput. Sci. (Math Games) 259, 663–670, MR1832815 (2002b:91025). 1498. L. E. Shader [1978], Another strategy for SIM, Math. Mag. 51, 60–64. 1499. L. E. Shader and M. L. Cook [1980], A winning strategy for the second

player in the game Tri-tip, Proc. Tenth S.E. Conference on Computing, Combinatorics and Graph Theory, Utilitas, Winnipeg.

1500. A. S. Shaki [1979], Algebraic solutions of partizan games with cycles,

Math. Proc. Camb. Phil. Soc. 85, 227–246. 1501. A. Shamir, R. L. Rivest and L. M. Adleman [1981], Mental Poker, in:

The Mathematical Gardner (D. A. Klarner, ed.), Wadsworth Internat., Belmont, CA, pp. 37–43.

1502. Y.-C. Shan, I.-C. Wu, H.-H. Lin and K.-Y. Kao [2012], Solving nine layer

Triangular Nim, JISE J. Inf. Sci. Eng. 28(1), 99–113, 2918941. 1503. A. Shankar and M. Sridharan [2005], New temparatures in Domineering,

Integers, Electr. J. of Combinat. Number Theory 5, #G04, 13 pp., Comb. Games Sect., MR2139167 (2006c:91036).

http://www.integers-ejcnt.org/vol5.html

1504. C. E. Shannon [1950], Programming a computer for playing chess, Philos.

Mag. (Ser. 7) 41, 256–275, MR0034095 (11,543f). 1505. A. Shapovalov [2011], Occupation games on graphs in which the second

player takes almost all vertices, Discrete Appl. Math. 159(15), 1526–1527, 2823909 (2012f:05202).

http://dx.doi.org/10.1016/j.dam.2011.03.002

1506. K. Shelton [2007], The game of take turn, de Gruyter, pp. 413–430, Proc. Integers Conference, Carrollton, Georgia, October 27-30,2005, in celebration of the 70th birthday of Ronald Graham. B. Landman, M. Nathanson, J. Nešetřil, R. Nowakowski, C. Pomerance eds., appeared also in Integers, Electr. J. of Combinat. Number Theory 7(20), special volume in honor of Ron Graham, #A31, 18 pp., MR2337065.

http://www.integers-ejcnt.org/vol7(2).html

1507. A. Shen [2000], Lights out, Math. Intelligencer 22 issue 3, 20–21. 1508. R. Sheppard and J. Wilkinson [1995], Strategy Games: A Collection Of 50

Games & Puzzles To Stimulate Mathematical Thinking, Parkwest Publications.

1509. G. J. Sherman [1978], A child’s game with permutations, Math. Mag. 51,

67–68. 1510. Z. Shi, W. Goddard, S. T. Hedetniemi, K. Kennedy, R. Laskar and

A. McRae [2005], An algorithm for partial Grundy number on trees, Discrete Math. 304(1-3), 108–116, 2184451 (2006h:05223).

http://dx.doi.org/10.1016/j.disc.2005.09.008

1511. W. L. Sibert and J. H. Conway [1992], Mathematical Kayles, Internat. J. Game Theory 20(3), 237–246, 1146325.

http://dx.doi.org/10.1007/BF01253778

1512. G. Sicherman [2002], Theory and practice of Sylver coinage, Integers, Electr. J. of Combinat. Number Theory 2, #G2, 8 pp., Comb. Games Sect., MR1934618 (2003h:05026).

http://www.integers-ejcnt.org/vol2.html

1513. N. Sieben [2004], Hexagonal polyomino weak (1, 2)-achievement games,

Acta Cybernet. 16(4), 579–585, MR2104074. 1514. N. Sieben [2004], Snaky is a 41-dimensional winner, Integers, Electr.

J. of Combinat. Number Theory 4, #G5, 4 pp., Comb. Games Sect., MR2116011.

http://www.integers-ejcnt.org/vol4.html

1515. N. Sieben [2008], Polyominoes with minimum site-perimeter and full set achievement games, European J. Combin. 29(1), 108–117, MR2368619 (2008j:05092).

http://dx.doi.org/10.1016/j.ejc.2006.12.008

1516. N. Sieben [2008], Proof trees for weak achievement games, Integers, Electr.

J of Combinat. Number Theory 8, G07, 18, MR2472080 (2010b:91054). 1517. N. Sieben and E. Deabay [2005], Polyomino weak achievement games on 3-

dimensional rectangular boards, Discrete Math. 290, 61–78, MR2117357 (2005h:05044).

1518. A. N. Siegel [2000], Combinatorial Game Suite, a software tool for investigating games.

http://cgsuite.sourceforge.net/

1519. A. N. Siegel [2006], Reduced canonical forms of stoppers, Electron. J. Combin. 13(1), #R57, 14 pp., MR2240763 (2007b:91030).

http://www.combinatorics.org/

1520. A. N. Siegel [2009], Backsliding Toads and Frogs, in: Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 197–214.

1521. A. N. Siegel [2009], Coping with cycles, in: Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 91–123.

1522. A. N. Siegel [2009], New results in loopy games, in: Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 215–232.

1523. A. N. Siegel [2013], Misère Canonical Forms of Partizan Games, in: Games

of No Chance 4 , Cambridge University Press, to appear. 1524. A. N. Siegel [2013], Misère Games and Misère Quotients, in: Games of

No Chance 4 , Cambridge University Press, to appear.

1525. A. N. Siegel [2013], The Structure and Classification of Misère Quotients,

in: Games of No Chance 4 , Cambridge University Press, to appear. 1526. R. Silber [1976], A Fibonacci property of Wythoff pairs, Fibonacci Quart.

14, 380–384. 1527. R. Silber [1977], Wythoff’s Nim and Fibonacci representations, Fibonacci

Quart. 15, 85–88. 1528. J.-N. O. Silva [1993], Some game bounds depending on birthdays, Portu-

galiae Math. 50, 353–358. 1529. R. Silver [1967], The group of automorphisms of the game of 3-

dimensional ticktacktoe, Amer. Math. Monthly 74, 247–254. 1530. D. L. Silverman [1971], Your Move, McGraw-Hill. 1531. G. J. Simmons [1969], The game of SIM, J. Recr. Math. 2, 66. 1532. D. Singmaster [1981], Almost all games are first person games, Eureka

41, 33–37. 1533. D. Singmaster [1982], Almost all partizan games are first person and

almost all impartial games are maximal, J. Combin. Inform. System Sci. 7, 270–274.

1534. D. Singmaster [1999], Some diophantine recreations, in: The Mathemagician and Pied Puzzler, honoring Martin Gardner; E. Berlekamp and T. Rodgers, eds., A K Peters, Natick, MA, pp. 219-235.

1535. A. Sinko and P. J. Slater [2006], Efficient domination in knights graphs,

AKCE Int. J. Graphs Comb. 3(2), 193–204, 2285466 (2007m:05190). 1536. A. Sinko and P. J. Slater [2008], Queen’s domination using border squares

and (A, B)-restricted domination, Discrete Math. 308(20), 4822–4828, 2438189 (2009f:05208).

http://dx.doi.org/10.1016/j.disc.2007.08.065

1537. W. Slany [2001], The complexity of graph Ramsey games, Proc. Intern. Conference on Computers and Games CG’2000 (T. Marsland and I. Frank, eds.), Vol. 2063, Hamamatsu, Japan, Oct. 2000, Lecture Notes in Computer Science, Springer, pp. 186–203, MR1909610.

1538. W. Slany [2002], Endgame problems of Sim-like graph Ramsey avoidance games are PSPACE-complete, Theoret. Comput. Sci. (Math Games) 289, 829–843, MR1933803 (2003h:05177).

1539. C. A. B. Smith [1966], Graphs and composite games, J. Combinatorial Theory 1, 51–81, reprinted in slightly modified form in: A Seminar on Graph Theory (F. Harary, ed.), Holt, Rinehart and Winston, New York, NY, 1967, pp. 86-111, 0194362 (33 #2572).

1540. C. A. B. Smith [1968], Compound games with counters, J. Recr. Math.

1, 67–77. 1541. C. A. B. Smith [1971], Simple game theory and its applications, Bull.

Inst. Math. Appl. 7, 352–357. 1542. D. E. Smith and C. C. Eaton [1911], Rithmomachia, the great medieval

number game, Amer. Math. Montly 18, 73–80.

1543. F. Smith and P. Stănică [2002], Comply/constrain games or games with a Muller twist, Integers, Electr. J. of Combinat. Number Theory 2, #G3, 10 pp., Comb. Games Sect., MR1945951 (2003i:91029).

http://www.integers-ejcnt.org/vol2.html

1544. R. Smullyan [2005], Gödelian puzzles, in: Tribute to a Mathemagician, honoring Martin Gardner (B. Cipra, E. D. Demaine, M. L. Demaine and T. Rodgers, eds.), A K Peters, Wellesley, MA, pp. 49-54.

1545. R. G. Snatzke [2002], Exhaustive search in Amazons, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 261–278, MR1973017.

1546. M. Soltys and C. Wilson [2011], On the complexity of computing winning strategies for finite poset games, Theory Comput. Syst. 48(3), 680–692, 2770813 (2012e:91016).

http://dx.doi.org/10.1007/s00224-010-9254-y

1547. R. Sosic and J. Gu [1990], A polynomial time algorithm for the n-queens

problem, SIGART 1 issue 3, 7–11. 1548. J. Spencer [1977], Balancing games, J. Combinatorial Theory Ser. B

23(1), 68–74, 0526057 (58 #26058). 1549. J. Spencer [1984], Guess a number with lying, Math. Mag. 57, 105–108. 1550. J. Spencer [1986], Balancing vectors in the max norm, Combinatorica 6,

55–65. 1551. J. Spencer [1991], Threshold spectra via the Ehrenfeucht game, Discrete

Appl. Math. 30(2-3), 235–252, ARIDAM III (New Brunswick, NJ, 1988), 1095377 (92b:03040).

http://dx.doi.org/10.1016/0166-218X(91)90048-2

1552. J. Spencer [1992], Ulam’s searching game with a fixed number of lies,

Theoret. Comput. Sci. (Math Games) 95, 307–321. 1553. J. Spencer [1994], Randomization, derandomization and antirandomiza-

tion: three games, Theoret. Comput. Sci. (Math Games) 131, 415–429. 1554. W. L. Spight [2001], Extended thermography for multiple kos in Go, Theo-

ret. Comput. Sci. 252(1-2), 23–43, Computer and games (Tsukuba, 1998), 1806224 (2001k:91041).

http://dx.doi.org/10.1016/S0304-3975(00)00075-X

1555. W. L. Spight [2002], Go thermography: the 4/21/98 Jiang-Rui endgame, in: More games of no chance (Berkeley, CA, 2000), Vol. 42 of Math. Sci. Res. Inst. Publ., Cambridge Univ. Press, Cambridge, pp. 89–105, 1973007 (2004d:91050).

1556. E. L. Spitznagel, Jr. [1967], A new look at the fifteen puzzle, Math. Mag.

40, 171–174. 1557. E. L. Spitznagel, Jr. [1973], Properties of a game based on Euclid’s algo-

rithm, Math. Mag. 46, 87–92. 1558. M. Z. Spivey [2009], Staircase rook polynomials and Cayley’s game of

Mousetrap, European J. Combin. 30(2), 532–539, 2489284 (2010f:05016).

http://dx.doi.org/10.1016/j.ejc.2008.04.005

1559. R. Sprague [1935–36], Über mathematische Kampfspiele, Tôhoku Math.

J. 41, 438–444. 1560. R. Sprague [1937], Über zwei Abarten von Nim, Tôhoku Math. J. 43,

351–354. 1561. R. Sprague [1947], Bemerkungen über eine spezielle Abelsche Gruppe,

Math. Z. 51, 82–84. 1562. R. Sprague [1961], Unterhaltsame Mathematik, Vieweg and Sohn, Braun-

schweig, Paperback reprint, translation by T. H. O’Beirne: Recreation in Mathematics, Blackie, 1963.

1563. R. G. Stanton [2004], Some design theory games, Bull. Inst. Combin.

Appl. 41, 61–63. 1564. H. Steinhaus [1960], Definitions for a theory of games and pursuit, Naval

Res. Logistics 7, 105–108. 1565. V. N. Stepanenko [1975], Grundy games under conditions of semidefinite-

ness, Cybernetics 11, 167–172 (trans. of Kibernetika 11 (1975) 145–149). 1566. B. M. Stewart [1939], Problem 3918 (k-peg tower of Hanoi), Amer. Math.

Monthly 46, 363, solution by J. S. Frame, ibid. 48 (1941) 216–217; by the proposer, ibid. 217–219.

1567. F. Stewart [2007], The sequential join of combinatorial games, Integers, Electr. J. of Combinat. Number Theory 7, #G03, 10 pp., MR2299809.

http://www.integers-ejcnt.org/vol7.html

1568. I. Stewart [1971], Solid knights tours, J. Recr. Math. 4(1), 1. 1569. I. Stewart [1991], Concentration: a winning strategy, Sci. Amer. 265,

167–172, October issue. 1570. I. Stewart [2000], Hex marks the spot, Sci. Amer. 283, 100–103, Septem-

ber issue. 1571. L. Stiller [1988], Massively parallel retrograde analysis, Tech. Rep. BU-CS

TR88–014, Comp. Sci. Dept., Boston University. 1572. L. Stiller [1989], Parallel analysis of certain endgames, Internat. Comp.

Chess Assoc. J. 12, 55–64. 1573. L. Stiller [1991], Group graphs and computational symmetry on massively

parallel architecture, J. Supercomputing 5, 99–117. 1574. L. Stiller [1996], Multilinear algebra and chess endgames, in: Games of

No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 151–192.

1575. D. L. Stock [1989], Merlin’s magic square revisited, Amer. Math. Monthly

96, 608–610. 1576. L. J. Stockmeyer and A. K. Chandra [1979], Provably difficult combina-

torial games, SIAM J. Comput. 8(2), 151–174, 529587 (80d:68060).

http://dx.doi.org/10.1137/0208013

1577. P. K. Stockmeyer [1994], Variations on the four-post Tower of Hanoi puzzle, Congr. Numer. 102, 3–12, Proc. 25th Southeastern Internat. Conf. on

Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1994). 1578. P. K. Stockmeyer [1999], The average distance between nodes in the cyclic

Tower of Hanoi digraph, Combinatorics, Graph Theory, and Algorithms, Vol. I, II (Kalamazoo, MI, 1996), New Issues Press, Kalamazoo, MI, pp. 799–808.

1579. P. K. Stockmeyer [2005], The Tower of Hanoi: a bibliography, Internet publication 38 pp.

http://www.cs.wm.edu/$\sim$pkstoc/{hpapers}.html

1580. P. K. Stockmeyer, C. D. Bateman, J. W. Clark, C. R. Eyster, M. T. Harrison, N. A. Loehr, P. J. Rodriguez and J. R. Simmons III [1995], Exchanging disks in the tower of Hanoi, Intern. J. Computer Math. 59, 37–47.

1581. K. B. Stolarsky [1976], Beatty sequences, continued fractions, and certain

shift operators, Canad. Math. Bull. 19, 473–482, MR0444558 (56 #2908). 1582. K. B. Stolarsky [1977], A set of generalized Fibonacci sequences such that

each natural number belongs to exactly one, Fibonacci Quart. 15, 224, MR0472674 (57 #12369).

1583. K. B. Stolarsky [1991], From Wythoff’s Nim to Chebyshev’s inequality,

Amer. Math. Monthly 98(10), 889–900, MR1137536 (93b:90132). 1584. J. A. Storer [1983], On the complexity of chess, J. Comput. System Sci.

27(1), 77–100, 730916 (85g:68030).

http://dx.doi.org/10.1016/0022-0000(83)90030-2

1585. W. E. Story [1879], Notes on the ”15” puzzle, Amer. J. Math. 2, 399–404. 1586. P. D. Straffin, Jr. [1985], Three-person winner-take-all games with Mc-

Carthy’s revenge rule, College J. Math. 16, 386–394. 1587. P. D. Straffin [1993], Game Theory and Strategy, New Mathematical Li-

brary, MAA, Washington, DC. 1588. P. D. Straffin, Jr. [1995], Position graphs for Pong Hau K’i and Mu Torere,

Math. Mag. 68, 382–386. 1589. T. Ströhlein and L. Zagler [1977], Analyzing games by Boolean matrix

iteration, Discrete Math. 19, 183–193. 1590. W. Stromquist [2007], Winning paths in N-by-infinity hex, Integers,

Electr. J. of Combinat. Number Theory 7, #G05, 3 pp., MR2299811.

http://www.integers-ejcnt.org/vol7.html

1591. W. Stromquist and D. Ullman [1993], Sequential compounds of combinatorial games, Theoret. Comput. Sci. 119(2), 311–321, 1244296 (94k:90171).

http://dx.doi.org/10.1016/0304-3975(93)90162-M

1592. K. Sugihara and I. Suzuki [1989], Optimal algorithms for a pursuit-evasion

problem in grids, SIAM J. Disc. Math. 2, 126–143. 1593. X. Sun [2002], Improvements on Chomp, Integers, Electr. J. of Combi-

nat. Number Theory 2, #G1, 8 pp., Comb. Games Sect., MR1917957 (2003e:05015).

http://www.integers-ejcnt.org/vol2.html

1594. X. Sun [2005], Wythoff’s sequence and N-heap Wythoff’s conjectures,

Discrete Math. 300, 180–195, MR2170125. 1595. X. Sun and D. Zeilberger [2004], On Fraenkel’s N-heap Wythoff’s con-

jectures, Ann. Comb. 8, 225–238, MR2079933 (2005e:91039). 1596. K. Sutner [1988], Additive automata on graphs, Complex Systems 2, 649–

661, MR987520 (90k:68127). 1597. K. Sutner [1988], On σ-automata, Complex Systems 2, 1–28. 1598. K. Sutner [1989], Linear cellular automata and the Garden-of-Eden, Math.

Intelligencer 11, 49–53. 1599. K. Sutner [1990], The σ-game and cellular automata, Amer. Math.

Monthly 97, 24–34. 1600. K. Sutner [1995], On the computational complexity of finite cellular au-

tomata, J. Comput. System Sci. 50, 87–97. 1601. K. Sutner [2001], Decomposition of additive cellular automata, Complex

Systems 13, 245–270, MR1916041 (2003e:37016). 1602. K. J. Swanepoel [2000], Balancing unit vectors, J. Combin. Theory

(Ser. A) 89, 105–112. 1603. Z. Szaniszlo, M. Tomova and C. Wyels [2009], The N-queens problem

on a symmetric Toeplitz matrix, Discrete Math. 309, 969–974, 2502208 (2010d:05023).

http://dx.doi.org/10.1016/j.disc.2008.01.042

1604. M. Szegedy [1999], In how many steps the k peg version of the towers of Hanoi game can be solved?, in: STACS 99, Trier, Lecture Notes in Computer Science, Vol. 1563, Springer, Berlin, pp. 356–361.

1605. G. J. Székely and M. L. Rizzo [2007], The uncertainty principle of game

theory, Amer. Math. Monthly 114(8), 688–702, MR2354439. 1606. L. A. Székely [1984], On two concepts of discrepancy in a class of com-

binatorial games, in: Finite and infinite sets, Vol. I, II (Eger, 1981), Vol. 37 of Colloq. Math. Soc. János Bolyai, North-Holland, Amsterdam, pp. 679–683, 818270 (87f:05161).

1607. J. L. Szwarcfiter and G. Chaty [1994], Enumerating the kernels of a di-

rected graph with no odd circuits, Inform. Process. Lett. 51, 149–153. 1608. W. Szumny, I. Włoch and A. Włoch [2008], On the existence and on the

number of (k, l)-kernels in the lexicographic product of graphs, Discrete Math. 308(20), 4616–4624, 2438167 (2009e:05235).

http://dx.doi.org/10.1016/j.disc.2007.08.078

1609. A. Takahashi, S. Ueno and Y. Kajitani [1995], Mixed searching and

proper-path-width, Theoret. Comput. Sci. (Math Games) 137, 253–268. 1610. T. Takizawa [2002], An application of mathematical game theory to Go

endgames: some width-two-entrance rooms with and without kos, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 108–124, MR1973008.

1611. G. Tardos [1988], Polynomial bound for a chip firing game on graphs, SIAM J. Discrete Math. 1(3), 397–398, 955655 (89i:68103).

http://dx.doi.org/10.1137/0401039

1612. M. Tarsi [1983], Optimal search on some game trees, J. Assoc. Comput.

Mach. 30, 389–396. 1613. A. Taylor and W. Zwicker [1995], Simple games and magic squares, J.

Combin. Theory Ser. A 71(1), 67–88, 1335777 (96c:90152).

http://dx.doi.org/10.1016/0097-3165(95)90016-0

1614. R. Telgársky [1987], Topological games: on the 50th anniversary of the

Banach-Mazur game, Rocky Mountain J. Math. 17, 227–276. 1615. T. Thanatipanonda [2008], How to beat Capablanca, Adv. in Appl. Math.

40, 266–270, 2388615.

http://dx.doi.org/10.1016/j.aam.2006.11.005

1616. T. Thanatipanonda [2011], Further hopping with Toads and Frogs, Elec-

tron. J. Combin. 18(1), Paper 67, 12, 2788684. 1617. T. Thanatipanonda and D. Zeilberger [2009], A symbolic finite-state ap-

proach for automated proving of theorems in combinatorial game theory, J. Difference Equ. Appl. 15, 111–118, 2482841 (2010b:91055).

http://dx.doi.org/10.1080/10236190802006423

1618. W. F. D. Theron and G. Geldenhuys [1998], Domination by queens on a

square beehive, Discrete Math. 178, 213–220. 1619. K. Thompson [1986], Retrograde analysis of certain endgames, Internat.

Comp. Chess Assoc. J. 9, 131–139. 1620. H. Tohyama and A. Adachi [2000], Complexity of path discovery prob-

lems, Theoret. Comput. Sci. (Math Games) 237, 381–406. 1621. G. P. Tollisen and T. Lengyel [2000], Color switching games, Ars Combin.

56, 223–234, MR1768618 (2001b:05094). 1622. I. Tomescu [1990], Almost all digraphs have a kernel, Discrete Math. 84,

181–192. 1623. B. Torrence [2011], The easiest lights out games, College Math. J. 42,

361–372. 1624. R. Tošić and S. Šćekić [1983], An analysis of some partizan graph games,

Proc. 4th Yugoslav Seminar on Graph Theory, Novi Sad, pp. 311–319. 1625. S. P. Tung [1987], Computational complexities of Diophantine equations

with parameters, J. Algorithms 8, 324–336, MR905990 (88m:03063). 1626. A. M. Turing, M. A. Bates, B. V. Bowden and C. Strachey [1953], Digital

computers applied to games, in: Faster Than Thought (B. V. Bowden, ed.), Pitman, London, pp. 286–310.

1627. R. Uehara and S. Iwata [1990], Generalized Hi-Q is NP-complete, Trans.

IEICE E73, 270–273. 1628. J. Úlehla [1980], A complete analysis of von Neumann’s Hackendot, In-

ternat. J. Game Theory 9, 107–113. 1629. D. Ullman [1992], More on the four-numbers game, Math. Mag. 65, 170– 1630. J. V. Uspensky [1927], On a problem arising out of the theory of a certain

game, Amer. Math. Monthly 34, 516–521. 1631. S. Vajda [1992], Mathematical Games and How to Play Them, Ellis Hor-

wood Series in Mathematics and its Applications, Chichester, England. 1632. H. J. van den Herik and I. S. Herschberg [1985], The construction of an

omniscient endgame database, Internat. Comp. Chess Assoc. J. 8, 66–87. 1633. J. van den Heuvel [2001], Algorithmic aspects of a chip-firing game, Com-

bin. Probab. Comput. 10, 505–529, MR1869843 (2002h:05154). 1634. B. L. van der Waerden [1974], The game of rectangles, Ann. Mat. Pura

Appl. 98, 63–75, MR0351854 (50 #4342). 1635. J. van Leeuwen [1976], Having a Grundy-numbering is NP-complete, Re-

port No. 207, Computer Science Dept., Pennsylvania State University, University Park, PA.

1636. A. J. van Zanten [1990], The complexity of an optimal algorithm for the

generalized tower of Hanoi problem, Intern. J. Comput. Math. 36, 1–8. 1637. A. J. van Zanten [1991], An iterative optimal algorithm for the generalized

tower of Hanoi problem, Intern. J. Comput. Math. 39, 163–168. 1638. I. Vardi [1991], Computational Recreations in Mathematica, Addison Wes-

ley. 1639. L. P. Varvak [1968], A generalization of the concept of p-sum of graphs,

Dopovīdī Akad. Nauk Ukraïn. RSR Ser. A 1968, 965–968, MR0245468 (39 #6776).

1640. L. P. Varvak [1968], Games on the sum of graphs, Cybernetics 4, 49–51

(trans. of Kibernetika (Kiev) 4 (1968) 63–66), MR0299238 (45 #8287). 1641. L. P. Varvak [1970], A certain generalization of the Grundy function,

Kibernetika (Kiev) (5), 112–116, MR0295968 (45 #5029). 1642. L. P. Varvak [1971], Game properties of generalized p-sums of graphs,

Dopovīdī Akad. Nauk Ukraïn. RSR Ser. A pp. 1059–1061, 1148, MR0307731 (46 #6851).

1643. L. P. Varvak [1973], A certain generalization of the nucleus of a graph,

Ukrainian Math. J. 25, 78–81, MR0323649 (48 #2005). 1644. J. Veerasamy and I. Page [1994], On the towers of Hanoi problem with

multiple spare pegs, Intern. J. Comput. Math. 52, 17–22. 1645. H. Venkateswaran and M. Tompa [1989], A new pebble game that char-

acterizes parallel complexity classes, SIAM J. Comput. 18, 533–549. 1646. D. Viaud [1987], Une stratégie générale pour jouer au Master-Mind,

RAIRO Recherche opérationelle/Operations Research 21, 87–100. 1647. F. R. Villegas, L. Sadun and J. F. Voloch [2002], Blet: a mathematical

puzzle, Amer. Math. Monthly 109, 729–740. 1648. J. von Neumann [1928], Zur Theorie der Gesellschaftsspiele, Math. Ann.

100, 295–320. 1649. J. von Neumann and O. Morgenstern [2004], Theory of Games and Eco-

nomic Behaviour, Princeton University Press, Princeton, NJ, reprint of the 3rd 1980 edition; first edition appeared in 1944.

1650. R. G. Wahl [2005], The Butler University game, Tribute to a Mathema-

gician, A K Peters, Wellesley, pp. 37–40, honoring Martin Gardner. 1651. J. Waldmann [2002], Rewrite games, Rewriting Techniques and Appli-

cations, Copenhagen, 22-24 July 2002 (S. Tison, ed.), Vol. LNCS 2378, Lecture Notes in Computer Science, Springer, pp. 144–158.

1652. C. T. C. Wall [1955], Nim-arithmetic, Eureka no. 18 pp. 3–7. 1653. J. L. Walsh [1953], The name of the game of Nim, Letter to the Editor,

Math. Gaz. 37, 290. 1654. M. Walsh [2003], A note on the Grundy number, Bull. Inst. Combin.

Appl. 38, 23–26, 1977016 (2004c:05078). 1655. T. R. Walsh [1982], The towers of Hanoi revisited: moving the rings by

counting the moves, Inform. Process. Lett. 15, 64–67. 1656. T. R. Walsh [1983], Iteration strikes back at the cyclic towers of Hanoi,

Inform. Process. Lett. 16, 91–93. 1657. W.-F. Wang [2006], Edge-partitions of graphs of nonnegative character-

istic and their game coloring numbers, Discrete Math. 306, 262–270. 1658. X. Wang and Y. Wu [2007], Minimum light number of lit-only σ-game on

a tree, Theoret. Comput. Sci. 381, 292–300, MR2347414. 1659. X. Wang and Y. Wu [2010], Lit-only σ-game on pseudo-trees, Discrete

Appl. Math. 158(17), 1945–1952, 2721756 (2011i:05180).

http://dx.doi.org/10.1016/j.dam.2010.08.009

1660. I. M. Wanless [1997], On the periodicity of graph games, Australas. J.

Combin. 16, 113–123, MR1477524 (98i:05159). 1661. I. M. Wanless [2001], Path achievement games, Australas. J. Combin. 23,

9–18, MR1814595 (2002k:91050). 1662. R. H. Warren [1996], Disks on a chessboard, Amer. Math. Monthly 103,

305–307. 1663. A. Washburn [1990], Deterministic graphical games, J. Math. Anal. Appl.

153, 84–96. 1664. J. J. Watkins [1997], Knight’s tours on triangular honeycombs, Congr.

Numer. 124, 81–87, Proc. 28th Southeastern Internat. Conf. on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1997), MR1605097.

1665. J. J. Watkins [2000], Knight’s tours on cylinders and other surfaces, Congr. Numer. 143, 117–127, Proc. 31st Southeastern Internat. Conf. on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 2000), MR1817914 (2001k:05136).

1666. J. J. Watkins [2004], Across the Board: The Mathematics of Chessboard Problems, Princeton University Press, Princeton and Oxford, MR2041306 (2004m:00002).

1667. J. J. Watkins and R. L. Hoenigman [1997], Knight’s tours on a torus,

Math. Mag. 70, 175–184, MR1456114 (98i:00003). 1668. W. D. Weakley [1995], Domination in the queen’s graph, in: Graph theory,

Combinatorics, and Algorithms, Vol. 2 (Kalamazoo, MI, 1992) (Y. Alavi

and A. J. Schwenk, eds.), Wiley, New York, pp. 1223–1232. 1669. W. D. Weakley [2002], A lower bound for domination numbers of the

queen’s graph, J. Combin. Math. Combin. Comput. 43, 231–254. 1670. W. D. Weakley [2002], Upper bounds for domination numbers of the

queen’s graph, Discrete Math. 242, 229–243. 1671. W. A. Webb [1982], The length of the four-number game, Fibonacci

Quart. 20, 33–35, MR0660757 (84e:10017). 1672. M. Weimerskirch [2013], An Algorithm for Computing Indistinguishabil-

ity Quotients in Misère Impartial Combinatorial Games, in: Games of No Chance 4 , Cambridge University Press, to appear.

1673. C. P. Welter [1952], The advancing operation in a special abelian group,

Nederl. Akad. Wetensch. Proc. (Ser. A) 55 = Indag. Math.14, 304-314. 1674. C. P. Welter [1954], The theory of a class of games on a sequence of

squares, in terms of the advancing operation in a special group, Nederl. Akad. Wetensch. Proc. (Ser. A) 57 = Indag. Math.16, 194-200.

1675. J. West [1996], Champion-level play of domineering, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 85–91.

1676. J. West [1996], Champion-level play of dots-and-boxes, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 79–84, MR1427958.

1677. J. West [1996], New values for Top Entails, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 345–350.

1678. M. J. Whinihan [1963], Fibonacci Nim, Fibonacci Quart. 1(4), 9–13. 1679. R. Wilber [1988], White pebbles help, J. Comput. System Sci. 36, 108–

124. 1680. M. Wildon [2010], Knights, spies, games and ballot sequences, Discrete

Math. 310(21), 2974–2983, 2677658 (2011k:05014).

http://dx.doi.org/10.1016/j.disc.2010.07.005

1681. R. Wilfong [1991], Motion planning in the presence of movable obstacles. Algorithmic motion planning in robotics, Ann. Math. Artificial Intelligence 3, 131–150.

1682. R. M. Wilson [1974], Graph puzzles, homotopy and the alternating group,

J. Combin. Theory (Ser. B) 16, 86–96. 1683. P. Winkler [2002], Games people don’t play, in: Puzzler’s Tribute: a Feast

for the Mind, pp. 301–313, honoring Martin Gardner (D. Wolfe and T. Rodgers, eds.), A K Peters, Natick, MA, MR2034896 (2006c:00002).

1684. D. Wolfe [1993], Snakes in domineering games, Theoret. Comput. Sci. 119(2), 323–329, 1244297.

http://dx.doi.org/10.1016/0304-3975(93)90163-N

1685. D. Wolfe [1996], The gamesman’s toolkit, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 93–98.

http://www.gustavus.edu/$\sim$wolfe/games/

1686. D. Wolfe [2002], Go endgames are PSPACE-hard, in: More Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 42, Cambridge University Press, Cambridge, pp. 125–136, MR1973009 (2004b:91052).

1687. D. Wolfe [2009], On day n, in: Games of No Chance 3, Proc. BIRS Workshop on Combinatorial Games, July, 2005, Banff, Alberta, Canada, MSRI Publ. (M. H. Albert and R. J. Nowakowski, eds.), Vol. 56, Cambridge University Press, Cambridge, pp. 125–131.

1688. D. Wolfe and W. Fraser [2004], Counting the number of games, Theoret. Comp. Sci. 313, 527–532, special issue of Dagstuhl Seminar “Algorithmic Combinatorial Game Theory”, Feb. 2002, MR2056944.

1689. D. Wood [1981], The towers of Brahma and Hanoi revisited, J. Recr.

Math. 14, 17–24. 1690. D. Wood [1983], Adjudicating a towers of Hanoi contest, Intern. J. Com-

put. Math. 14, 199–207. 1691. J.-S. Wu and R.-J. Chen [1992], The towers of Hanoi problem with parallel

moves, Inform. Process. Lett. 44, 241–243. 1692. J.-S. Wu and R.-J. Chen [1993], The towers of Hanoi problem with cyclic

parallel moves, Inform. Process. Lett. 46, 1–6. 1693. J. Wu and X. Zhu [2006], Relaxed game chromatic number of outer planar

graphs, Ars Combin. 81, 359–367, MR2267825 (2007f:05067). 1694. J. Wu and X. Zhu [2008], Lower bounds for the game colouring number

of partial k-trees and planar graphs, Discrete Math. 308(12), 2637–2642, MR2410475 (2009c:05093).

http://dx.doi.org/10.1016/j.disc.2007.05.023

1695. J. Wu and X. Zhu [2008], The 6-relaxed game chromatic number of outerplanar graphs, Discrete Math. 308(24), 5974–5980, MR2464888 (2009j:91044).

http://dx.doi.org/10.1016/j.disc.2007.11.015

1696. Y. Wu [2009], Lit-only sigma game on a line graph, European J. Combin. 30(1), 84–95, 2460219 (2009k:91039).

http://dx.doi.org/10.1016/j.ejc.2008.02.003

1697. W. A. Wythoff [1907], A modification of the game of Nim, Nieuw Arch.

Wisk. 7, 199–202. 1698. A. M. Yaglom and I. M. Yaglom [1967], Challenging Mathematical Prob-

lems with Elementary Solutions, Vol. II, Holden-Day, San Francisco, translated from Russian by J. McCawley, Jr., revised and edited by B. Gordon.

1699. T. Yamada and K. Sakai [2006], On flatness and tameness of classes of impartial games, Publ. Res. Inst. Math. Sci. 42(2), 383–390, 2250065 (2007c:91040).

http://projecteuclid.org/getRecord?id=euclid.prims/
1166642107

1700. Y. Yamasaki [1978], Theory of division games, Publ. Res. Inst. Math.

Sciences, Kyoto Univ. 14, 337–358. 1701. Y. Yamasaki [1980], On misère Nim-type games, J. Math. Soc. Japan 32,

461–475. 1702. Y. Yamasaki [1981], The projectivity of Y -games, Publ. Res. Inst. Math.

Sciences, Kyoto Univ. 17, 245–248. 1703. Y. Yamasaki [1981], Theory of Connexes I, Publ. Res. Inst. Math. Sci-

ences, Kyoto Univ. 17, 777–812. 1704. Y. Yamasaki [1985], Theory of connexes II, Publ. Res. Inst. Math. Sci-

ences, Kyoto Univ. 21, 403–409. 1705. Y. Yamasaki [1989], Combinatorial Games: Back and Front, Springer

Verlag, Tokyo (in Japanese). 1706. Y. Yamasaki [1989], Shannon switching games without terminals II,

Graphs Combin. 5, 275–282. 1707. Y. Yamasaki [1991], A difficulty in particular Shannon-like games, Dis-

crete Appl. Math. 30, 87–90. 1708. Y. Yamasaki [1992], Shannon switching games without terminals III,

Graphs Combin. 8, 291–297. 1709. Y. Yamasaki [1993], Shannon-like games are difficult, Discrete Math. 111,

481–483. 1710. Y. Yamasaki [1997], The arithmetic of reversed positional games, The-

oret. Comput. Sci. (Math Games) 174, 247–249, also in Discrete Math. 165/166 (1997) 639–641.

1711. B. Yang, D. Dyer and B. Alspach [2004], Sweeping graphs with large clique number, in: Algorithms and computation, Vol. 3341 of Lecture Notes in Comput. Sci., Springer, Berlin, pp. 908–920, 2158389.

http://dx.doi.org/10.1007/978-3-540-30551-4_77

1712. B. Yang, D. Dyer and B. Alspach [2009], Sweeping graphs with large clique number, Discrete Math. 309(18), 5770–5780, 2567982 (2010k:05324).

http://dx.doi.org/10.1016/j.disc.2008.05.033

1713. C. Yang [2011], Sliding puzzles and rotating puzzles on graphs, Discrete Math. 311(14), 1290–1294, 2795539 (2012f:05139).

http://dx.doi.org/10.1016/j.disc.2011.03.011

1714. D.-q. Yang [2005], The complete game coloring number of the line graph of a forest, J. Fuzhou Univ. Nat. Sci. Ed. 33(2), 135–138, 2139826 (2005m:05099).

1715. D. Yang [2009], Activation strategy for relaxed asymmetric coloring games, Discrete Math. 309, 3323–3335, 2526751 (2010g:05247).

http://dx.doi.org/10.1016/j.disc.2008.09.047

1716. D. Yang [2009], Relaxed very asymmetric coloring games, Discrete Math.

309, 1043–1050, 2493523 (2010d:05064).

http://dx.doi.org/10.1016/j.disc.2007.11.058

1717. D. Yang [2012], Coloring games on squares of graphs, Discrete Math. 312,

1400–1406. 1718. D. Yang and H. A. Kierstead [2008], Asymmetric marking games in line

graphs, Discrete Math. 308(9), 1751–1755, MR2392616 (2009a:05081).

http://dx.doi.org/10.1016/j.disc.2007.03.082

1719. D. Yang and X. Zhu [2008], Activation strategy for asymmetric marking games, European J. Combin. 29, 1123–1132, MR2419216 (2009b:91039).

http://dx.doi.org/10.1016/j.ejc.2007.07.004

1720. D. Yang and X. Zhu [2010], Game colouring directed graphs, Electron. J. Combin. 17(1), Research Paper 11, 19, 2578906 (2011d:05150).

http://www.combinatorics.org/Volume_17/Abstracts/v17i1r11.
html

1721. J. Yang, S. Liao and M. Pawlak [2001], On a decomposition method for finding winning strategy in Hex game, in: Proceedings ADCOG: Internat. Conf. Application and Development of Computer Games (A. L. W. Sing, W. H. Man and W. Wai, eds.), City University of Honkong, pp. 96–111.

1722. Y. Ye, M. Zhai and Y. Zhang [2012], Pebbling number of squares of odd

cycles, Discrete Math. 312(21), 3174–3178. 1723. Y. Ye, P. Zhai and Y. Zhang [2012], Pebbling number of squares of even

cycles, Discrete Math. 312(21), 3203–3211. 1724. L. J. Yedwab [1985], On playing well in a sum of games, M.Sc. Thesis,

MIT, MIT/LCS/TR-348. 1725. Y. N. Yeh [1995], A remarkable endofunction involving compositions,

Stud. Appl. Math 95, 419–432. 1726. Y. Yesha [1978], Theory of annihilation games, Ph.D. Thesis, Weizmann

Institute of Science, Rehovot, Israel. 1727. Y. K. Yu and R. B. Banerji [1982], Periodicity of Sprague–Grundy func-

tion in graphs with decomposable nodes, Cybernetics and Systems: An Internat. J. 13, 299–310.

1728. S. Zachos [1988], Probabilistic quantifiers and games, J. Comput. System

Sci. 36, 433–451. 1729. M. Zaker [2005], Grundy chromatic number of the complement of bipartite

graphs, Australas. J. Combin. 31, 325–329, MR2113717 (2005h:05087). 1730. M. Zaker [2006], Results on the Grundy chromatic number of graphs,

Discrete Math. 306(23), 3166–3173, MR2273147. 1731. D. Zeilberger [2001], Three-rowed Chomp, Adv. in Appl. Math. 26, 168–

179, MR1808446 (2001k:91009). 1732. D. Zeilberger [2004], Chomp, recurrences and chaos(?), J. Difference Equ.

Appl. 10, 1281–1293, MR2100728 (2005g:39014). 1733. E. Zermelo [1913], Über eine Anwendung der Mengenlehre auf die Theorie

des Schachspiels, Proc. 5th Int. Cong. Math. Cambridge 1912 , Vol. II, Cambridge University Press, pp. 501–504.

1734. X. Zhu [1999], The game coloring number of planar graphs, J. Combin.

Theory (Ser. B) 75, 245–258, MR1676891 (99m:05064). 1735. X. Zhu [2000], The game coloring number of pseudo partial k-trees, Dis-

crete Math. 215, 245–262, MR1746462 (2000m:05102). 1736. X. Zhu [2008], Game coloring the Cartesian product of graphs, J. Graph

Theory 59, 261–278, MR2463181 (2009h:05095).

http://dx.doi.org/10.1002/jgt.20338

1737. X. Zhu [2008], Refined activation strategy for the marking game, J. Combin. Theory Ser. B 98(1), 1–18, 2368019 (2008k:91049).

http://dx.doi.org/10.1016/j.jctb.2007.04.004

1738. M. Zieve [1996], Take-away games, in: Games of No Chance, Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ. (R. J. Nowakowski, ed.), Vol. 29, Cambridge University Press, Cambridge, pp. 351–361.

1739. U. Zwick [2002], Jenga, Proceedings of SODA 2002 , pp. 243–246. 1740. U. Zwick and M. S. Paterson [1993], The memory game, Theoret. Comput.

Sci. (Math Games) 110, 169–196. 1741. U. Zwick and M. S. Paterson [1996], The complexity of mean payoff games

on graphs, Theoret. Comput. Sci. (Math Games) 158, 343–359. 1742. W. S. Zwicker [1987], Playing games with games: the hypergame paradox,

Amer. Math. Monthly 94, 507–514.