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y(damen)n(tal)34 b(notion)h(of)g Fi(sum)41 b Fj(\(disjunctiv)n(e)35 b(comp)r(ound\))h(of)f(games.)58 b(A)35 b(sum)g(is)g(a)g(\014nite)515 5006 y(collection)e(of)h(disjoin)n(t)g(games;)j(often)d(v)n(ery)f (basic,)i(simple)f(games.)55 b(Eac)n(h)33 b(of)h(the)h(t)n(w)n(o)p eop %%Page: 3 3 3 2 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina)-6 b(torics)32 b(#DS2)791 b Fj(3)515 523 y(pla)n(y)n(ers,)28 b(at)h(ev)n(ery)e(turn,)j(selects)f(one)g(of)g(the)h(games)e(and)h(mak) n(es)f(a)h(mo)n(v)n(e)f(in)h(it.)42 b(If)30 b(the)515 623 y(outcome)25 b(is)h(not)f(a)g(dra)n(w,)h(the)g(sum-game)e(ends)i (when)g(there)f(is)h(no)f(mo)n(v)n(e)g(left)h(in)g(an)n(y)f(of)515 722 y(the)30 b(comp)r(onen)n(t)f(games.)42 b(If)30 b(the)g(outcome)f (is)g(not)h(a)f(tie)h(either,)g(then)g(in)g Fi(normal)39 b Fj(pla)n(y)-7 b(,)515 822 y(the)33 b(pla)n(y)n(er)e(\014rst)h(unable) h(to)f(mo)n(v)n(e)g(loses)f(and)i(the)g(opp)r(onen)n(t)f(wins.)52 b(The)33 b(outcome)f(is)515 922 y(rev)n(ersed)26 b(in)h 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Fk(3)134 b(Breaking)46 b(the)f(Rules)515 2100 y Fj(As)24 b(the)g(exp)r(erts)f(kno)n(w,)h(some)f(of)h(the)g(most) g(exciting)f(games)g(are)f(obtained)i(b)n(y)f(breaking)515 2200 y(some)29 b(of)g(the)h(rules)e(for)h(com)n(binatorial)f(games,)g (suc)n(h)h(as)g(p)r(ermitting)h(a)f(pla)n(y)n(er)f(to)h(pass)515 2299 y(a)j(b)r(ounded)g(or)g(un)n(b)r(ounded)g(n)n(um)n(b)r(er)g(of)h (times,)g(i.e.,)h(relaxing)d(the)h(requiremen)n(t)g(that)515 2399 y(pla)n(y)n(ers)22 b(pla)n(y)i(alternately;)h(or)f(p)r(ermitting)h (a)f(n)n(um)n(b)r(er)g(of)g(pla)n(y)n(ers)f(other)h(than)h(t)n(w)n(o.) 35 b(But)515 2499 y(b)n(y)c(far)h(the)g(most)g(fruitful)h(tamp)r(ering) e(with)i(the)f(rules)f(seems)h(to)g(b)r(e)g(to)g(p)r(ermit)g(sums)515 2598 y(of)g(games)g(that)g(are)g(not)g(quite)h(\014xed)g(\(whic)n(h)f (explains)g(wh)n(y)h(mis)n(\022)-39 b(ere)30 b(pla)n(y)i(of)h(sums)f (of)515 2698 y(games)e(is)i(m)n(uc)n(h)g(harder)e(than)i(normal)f(pla)n (y\))h(or)e(not)i(quite)g(disjoin)n(t)g(\(W)-7 b(elter\))33 b(or)e(the)515 2798 y(game)c(do)r(es)g(not)g(seem)h(to)f(decomp)r(ose)g (in)n(to)g(a)h(sum)f(\(Geograph)n(y)f(or)h(P)n(oset)f(Games\).)639 2906 y(But)k(p)r(ermitting)g(a)f(pa)n(y)n(o\013)g(function)h(other)f (than)h(\(0,)14 b(1\))25 b(=)h(\(lose,)14 b(win\))30 b(or)f(\()3123 2873 y Fd(1)p 3123 2887 34 4 v 3123 2934 a(2)3166 2906 y Fe(;)3213 2873 y Fd(1)p 3213 2887 V 3213 2934 a(2)3256 2906 y Fj(\))d(=)515 3005 y(\(dra)n(w,)46 b(dra)n(w\))32 b(usually)-7 b(,)33 b(but)f(not)h(alw)n(a)n(ys,)e(leads) h(to)g(games)f(that)i(are)e(not)h(considered)515 3105 y(to)27 b(b)r(e)h(com)n(binatorial)e(games,)h(or)f(to)i(b)r(orderline)f (cases.)515 3388 y Fk(4)134 b(Wh)l(y)45 b(Is)g(the)g(Bibliograph)l(y)h (V)-11 b(ast?)515 3578 y Fj(In)31 b(the)h(realm)e(of)i(existen)n(tial)e (problems,)i(suc)n(h)f(as)g(sorting)f(or)g(T)-7 b(ra)n(v)n(eling)29 b(Salesp)r(erson,)515 3677 y(most)f(presen)n(t-da)n(y)f(in)n(teresting) h(decision)g(problems)g(can)g(b)r(e)h(classi\014ed)f(in)n(to)h (tractable,)515 3777 y(conditionally)f(in)n(tractable,)g(and)h(pro)n(v) -5 b(ably)28 b(in)n(tractable)g(ones.)40 b(There)29 b(are)f (exceptions,)515 3877 y(to)i(b)r(e)i(sure,)f(e.g.)f(graph)g (isomorphism)g(and)h(primalit)n(y)f(testing,)i(whose)e(complexit)n(y)g (is)515 3976 y(still)25 b(unkno)n(wn.)36 b(But)25 b(the)h(exceptions)e (are)h(few.)36 b(It)25 b(app)r(ears)f(that,)i(in)g(con)n(trast,)e (there)h(is)515 4076 y(a)e(v)n(ery)g(large)g(set)h(of)g(games)f(whose)h (complexities)f(are)g(hard)h(to)g(determine.)36 b(W)-7 b(e)24 b(call)g(the)515 4176 y(set)e(of)h(these)f(games)g Fi(Wonderland)p Fj(,)j(b)r(ecause)d(w)n(e)g(are)f(w)n(ondering)g(ab)r (out)i(the)g(complexit)n(y)515 4275 y(classi\014cation)38 b(of)j(its)f(mem)n(b)r(ers.)74 b(Only)40 b(few)g(games)f(ha)n(v)n(e)g (b)r(een)h(classi\014ed)g(in)n(to)g(the)515 4375 y(complexit)n(y)30 b(classes)g(they)h(b)r(elong)g(to.)46 b(T)-7 b(o)r(da)n(y)g(,)31 b(most)g(games)f(b)r(elong)h(to)g(W)-7 b(onderland,)515 4474 y(and)31 b(despite)h(recen)n(t)e(impressiv)n(e)h(progress,)f(the)i (to)r(ols)f(for)f(reducing)h(W)-7 b(onderland)31 b(are)515 4574 y(still)d(few)g(and)f(inadequate.)639 4682 y(T)-7 b(o)40 b(giv)n(e)g(an)g(example,)j(man)n(y)d(in)n(teresting)f(games)h (ha)n(v)n(e)f(a)h(v)n(ery)f(succinct)h(input)515 4782 y(size,)29 b(so)g(a)g(p)r(olynomial)g(strategy)f(is)i(often)f(more)g (di\016cult)h(to)g(come)f(b)n(y)g(\(Octal)g(games;)515 4881 y(Grundy's)g(game\).)41 b(Succinctness)29 b(and)g(non-disjoin)n (tness)f(of)h(games)g(in)g(a)g(sum)g(ma)n(y)g(b)r(e)515 4981 y(presen)n(t)d(sim)n(ultaneously)g(\(p)r(oset)g(games\).)36 b(In)27 b(general,)f(\\breaking)e(the)k(rules")d(and)i(the)p eop %%Page: 4 4 4 3 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina)-6 b(torics)32 b(#DS2)791 b Fj(4)515 523 y(alternating)28 b(quan)n(ti\014ers)f(add)i(to)g(the)g(v)n(olume)f(of)h(W)-7 b(onderland.)40 b(W)-7 b(e)29 b(susp)r(ect)h(that)f(the)515 623 y(large)19 b(size)i(of)f(W)-7 b(onderland,)22 b(a)f(fact)g(of)f (indep)r(enden)n(t)i(in)n(terest,)g(is)f(the)g(main)g(con)n(tributing) 515 722 y(factor)27 b(to)g(the)h(bulk)g(of)f(the)h(bibliograph)n(y)e (on)i(games.)515 1005 y Fk(5)134 b(Wh)l(y)45 b(Isn't)h(it)f(Larger?)515 1195 y Fj(The)30 b(bibliograph)n(y)e(b)r(elo)n(w)h(is)h(a)g(partial)f (list)h(of)f(b)r(o)r(oks)h(and)f(articles)g(on)h(com)n(binatorial)515 1295 y(games)d(and)g(related)g(material.)37 b(It)29 b(is)e(partial)g (not)h(only)g(b)r(ecause)f(I)h(constan)n(tly)f(learn)g(of)515 1395 y(additional)h(relev)-5 b(an)n(t)29 b(material)f(I)h(did)g(not)g (kno)n(w)g(ab)r(out)g(previously)-7 b(,)28 b(but)i(also)d(b)r(ecause) 515 1494 y(of)32 b(certain)h(self-imp)r(osed)f(restrictions.)51 b(The)33 b(most)g(imp)r(ortan)n(t)f(of)h(these)g(is)f(that)h(only)515 1594 y(pap)r(ers)27 b(with)i(some)e(original)g(and)h(non)n(trivial)f (mathematical)g(con)n(ten)n(t)h(are)f(considered.)515 1693 y(This)35 b(excludes)g(most)h(historical)e(reviews)h(of)g(games)g (and)g(most,)i(but)f(not)g(all,)h(of)f(the)515 1793 y(w)n(ork)31 b(on)i(heuristic)g(or)g(arti\014cial)f(in)n(telligence)h(approac)n(hes) e(to)i(games,)g(esp)r(ecially)g(the)515 1893 y(large)26 b(literature)h(concerning)g(computer)h(c)n(hess.)37 b(I)28 b(ha)n(v)n(e,)f(ho)n(w)n(ev)n(er,)f(included)i(the)h(com-)515 1992 y(p)r(endium)24 b(Levy)e([1988],)g(whic)n(h,)i(with)f(its)g(50)f (articles)g(and)h(extensiv)n(e)f(bibliograph)n(y)-7 b(,)22 b(can)515 2092 y(serv)n(e)31 b(as)g(a)h(\014rst)g(guide)g(to)g(this)g (w)n(orld.)50 b(Also)31 b(some)h(pap)r(ers)f(on)h(c)n(hess-endgames)e (and)515 2192 y(clev)n(er)c(exhaustiv)n(e)h(computer)g(searc)n(hes)f (of)h(some)g(games)g(ha)n(v)n(e)f(b)r(een)i(included.)639 2299 y(On)f(the)g(other)g(hand,)g(pap)r(ers)f(on)g(games)g(that)h (break)f(some)h(of)f(the)i(rules)e(of)h(com)n(bi-)515 2399 y(natorial)f(games)h(are)g(included)h(lib)r(erally)-7 b(,)28 b(as)f(long)g(as)h(they)g(are)f(in)n(teresting)g(and)h(retain) 515 2499 y(a)g(com)n(binatorial)e(\015a)n(v)n(or.)38 b(These)28 b(are)f(v)-5 b(ague)28 b(and)g(hard)g(to)g(de\014ne)h (criteria,)f(y)n(et)g(com)n(bi-)515 2598 y(natorialists)h(usually)h (recognize)f(a)h(com)n(binatorial)f(game)h(when)h(they)g(see)f(it.)47 b(Besides,)515 2698 y(it)30 b(is)g(in)n(teresting)f(to)g(break)g(also)g (this)h(rule)f(sometimes!)43 b(W)-7 b(e)30 b(ha)n(v)n(e)f(included)h (some)g(ref-)515 2798 y(erences)24 b(to)h(one-pla)n(y)n(er)e(games,)i (e.g.,)h(to)n(w)n(ers)e(of)h(Hanoi,)g Fe(n)p Fj(-queen)g(problems,)g (15-puzzle)515 2897 y(and)33 b(p)r(eg-solitaire,)g(but)h(only)f(few)g (zero-pla)n(y)n(er)d(games)j(\(suc)n(h)g(as)f(Life)i(and)f(games)f(on) 515 2997 y(\\sand)d(piles"\).)44 b(W)-7 b(e)31 b(ha)n(v)n(e)e(also)g (included)h(pap)r(ers)g(on)g(v)-5 b(arious)29 b(applications)g(of)h (games,)515 3096 y(esp)r(ecially)38 b(when)i(the)g(connection)e(to)i (games)e(is)h(substan)n(tial)g(or)f(the)i(application)e(is)515 3196 y(imp)r(ortan)n(t.)639 3304 y(In)28 b(1990,)e Fi(The)l(or)l(etic)l (al)31 b(Computer)f(Scienc)l(e)k Fj(inaugurated)26 b(a)i(Mathematical)f (Games)515 3404 y(Section)h(whose)f(main)h(purp)r(ose)f(is)h(to)f (publish)i(pap)r(ers)e(on)g(com)n(binatorial)f(games.)37 b(The)515 3503 y(\\Aims)d(and)f(Scop)r(e")h(and)g(the)g(names)g(and)f (addresses)g(of)h(the)g(Mathematical)g(Games)515 3603 y(Section)22 b(editors)g(are)f(prin)n(ted)i(in)f(the)h(\014rst)f(issue) g(of)h(ev)n(ery)e(v)n(olume)h(of)g(TCS.)h(Prosp)r(ectiv)n(e)515 3703 y(authors)k(are)g(in)n(vited)h(to)g(submit)h(their)f(pap)r(ers)g (b)n(y)f(email)h(\(p)r(ostscript)h(is)f(preferred\))f(or)515 3802 y(snailmail)c(\(in)h(triplicate\),)h(to)e(one)g(of)h(the)g (editors)f(whose)g(in)n(terests)g(seem)g(closest)g(to)h(the)515 3902 y(\014eld)i(co)n(v)n(ered)f(b)n(y)h(the)h(pap)r(er.)36 b(This)26 b(forum)h(is)f(b)r(eginning)g(to)h(b)r(ecome)f(a)g(fo)r(cal)g (p)r(oin)n(t)h(for)515 4001 y(high-class)22 b(researc)n(h)f(results)i 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b(to)g(the)g(facts)g(stated)g(in)g(Section)g(6,)i(hard)d (copies)h(of)f(the)i(bibliograph)n(y)d(are)h(not)515 3038 y(mailed)27 b(out)f(an)n(y)h(more,)f(with)h(the)h(p)r(ossible)e (exception)h(of)g(a)f(few)h(copies)f(to)h(individuals)515 3138 y(without)h(access)e(to)i(the)g(In)n(ternet.)639 3246 y(Most)k(of)g(the)h(bibliographic)e(en)n(tries)g(refer)h(to)g (items)g(written)g(in)h(English,)f(though)515 3346 y(there)20 b(is)g(a)f(sprinkling)h(of)g(Danish,)h(Dutc)n(h,)i(F)-7 b(renc)n(h,)21 b(German,)g(Japanese,)f(Slo)n(v)-5 b(akian)19 b(and)515 3445 y(Russian,)26 b(as)f(w)n(ell)h(as)g(some)f(English)g (translations)g(from)h(Russian.)36 b(The)26 b(predominance)515 3545 y(of)34 b(English)f(ma)n(y)g(b)r(e)h(due)g(to)g(certain)f (prejudices,)i(but)f(it)h(also)d(re\015ects)i(the)g(fact)g(that)515 3644 y(no)n(w)n(ada)n(ys)g(the)j Fi(lingua)h(fr)l(anc)l(a)44 b Fj(of)36 b(science)g(is)h(English.)63 b(In)36 b(an)n(y)g(case,)i(I'm) f(soliciting)515 3744 y(also)c(pap)r(ers)h(in)h(languages)e(other)h 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y(bibliograph)n(y)34 b(for)h(the)i(b)r(o)r(ok)e Fi(Combinatorial)40 b(Games)p Fj(,)f(AMS)d(Short)g(Course)e(Lecture)515 4807 y(Notes,)25 b(Summer)f(1990,)g(Ohio)g(State)g(Univ)n(ersit)n(y)-7 b(,)25 b(Colum)n(bus,)g(OH,)f Fi(Pr)l(o)l(c.)k(Symp.)g(Appl.)515 4906 y(Math.)39 b Fc(43)d Fj(\(R.)i(K.)f(Guy)-7 b(,)41 b(ed.\),)f(AMS)e(1991,)g(pp.)g(191{226)c(with)j(400)f(items,)41 b(and)c(in)p eop %%Page: 6 6 6 5 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina)-6 b(torics)32 b(#DS2)791 b Fj(6)515 523 y(the)30 b Fi(Dynamic)i(Surveys)k Fj(section)30 b(of)f(the)h Fi(Ele)l(ctr)l(onic)j(J.)e(of)i (Combinatorics)38 b Fj(in)30 b(No)n(v)n(em-)515 623 y(b)r(er)37 b(1994)f(with)i(542)f(items)h(\(up)r(dated)g(there)g(at)g(o)r(dd)f (times\).)68 b(It)38 b(also)f(app)r(eared)g(as)515 722 y(the)d(master)g(bibliograph)n(y)e(in:)50 b Fi(Games)37 b(of)f(No)g(Chanc)l(e)p Fj(,)h(Pro)r(c.)c(MSRI)h(W)-7 b(orkshop)33 b(on)515 822 y(Com)n(binatorial)22 b(Games,)i(July)-7 b(,)25 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b(with)i(email)e(addresses)f(and)h(URLs,)h(where)f(a)n(v)-5 b(ailable.)639 2109 y(One)38 b(corresp)r(onden)n(t)e(and)i(m)n(yself)g (think)g(that)g(the)h(bibliograph)n(y)d(has,)k(after)e(the)515 2208 y(August)27 b(1995)f(up)r(date,)i(b)r(ecome)g(somewhat)f(un)n (wieldy:)639 2316 y(1.)f(Should)h(henceforth)f(new)g(additions)g(b)r(e) g(k)n(ept)h(in)f(separate)f(\014les?)36 b(Disadv)-5 b(an)n(tage:)515 2416 y(mac)n(hine)26 b(searc)n(hing)e(will)j(ha)n(v)n(e)e(to)i(b)r(e)g (done)f(on)g(sev)n(eral)f(\(.tex\))i(\014les,)f(and)h(visual)f(searc)n (h)515 2515 y(on)32 b(sev)n(eral)f(.ps)i(\014les.)53 b(Ho)n(w)n(ev)n(er,)32 b(some)g(of)h(the)g(older)f(up)r(dates)h(ma)n(y) f(b)r(e)i(merged)e(with)515 2615 y(the)c(main)f(part,)g(after)h(a)f (while.)639 2723 y(2.)20 b(The)g(bibliograph)n(y)f(could)h(b)r(e)h (brok)n(en)e(up)h(in)n(to)g(sections)g(of)g(related)g(pap)r(ers.)33 b(Th)n(us,)515 2823 y(zero-p)r(erson)27 b(and)j(one-p)r(erson)e(games)h 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(p)r(oin)n(ts?)515 3911 y Fk(9)134 b(Ac)l(kno)l(wledgmen)l(ts)515 4101 y Fj(Man)n(y)35 b(p)r(eople)h(suggested)f(additions)h(to)g(the)g (bibliograph)n(y)-7 b(,)37 b(or)e(con)n(tributed)g(to)h(it)h(in)515 4200 y(other)18 b(w)n(a)n(ys.)32 b(Among)18 b(them)h(are:)32 b(Ak)n(eo)17 b(Adac)n(hi,)k(Ingo)c(Alth\177)-42 b(ofer,)21 b(Thomas)d(Andreae,)h(Eli)515 4300 y(Bac)n(hm)n(upsky)-7 b(,)27 b(Adriano)h(Barlotti,)f(J\023)-42 b(ozsef)28 b(Bec)n(k,)g (Claude)g(Berge,)f(Gerald)h(E.)g(Bergum,)515 4400 y(H.)g(S.)h (MacDonald)f(Co)n(xeter,)f(Thomas)g(S.)i(F)-7 b(erguson,)27 b(James)g(A.)i(Flanigan,)e(F)-7 b(red)29 b(Gal-)515 4499 y(vin,)d(Martin)g(Gardner,)g(Alan)g(J.)g(Goldman,)g(Solomon)f(W.)i (Golom)n(b,)f(Ric)n(hard)f(K.)h(Guy)-7 b(,)515 4599 y(Shigeki)24 b(Iw)n(ata,)g(Da)n(vid)h(S.)f(Johnson,)h(Victor)f(Klee,)h(Donald)f(E.)g (Kn)n(uth,)h(An)n(ton)g(Kotzig,)515 4699 y(Je\013)33 b(C.)h(Lagarias,)e(Mic)n(hel)h(Las)g(V)-7 b(ergnas,)34 b(Hendrik)f(W.)h(Lenstra,)g(Hermann)f(Loimer,)515 4798 y(F.)28 b(Lo)r(c)n(kw)n(o)r(o)r(d)f(Morris,)f(Ric)n(hard)i(J.)f(No)n(w) n(ak)n(o)n(wski,)f(Judea)h(P)n(earl,)g(J.)g(Mic)n(hael)h(Robson,)515 4898 y(Da)n(vid)34 b(Singmaster,)h(W)-7 b(olfgang)34 b(Slan)n(y)-7 b(,)36 b(Cedric)e(A.)h(B.)f(Smith,)k(Rastisla)n(w)33 b(T)-7 b(elg\023)-42 b(arsky)-7 b(,)515 4997 y(Y\026)-42 b(ohei)23 b(Y)-7 b(amasaki)22 b(and)h(man)n(y)f(others.)35 b(Thanks)22 b(to)h(all)g(and)g(k)n(eep)g(up)g(the)g(game!)35 b(Sp)r(ecial)p eop %%Page: 7 7 7 6 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina)-6 b(torics)32 b(#DS2)791 b Fj(7)515 523 y(thanks)28 b(are)g(due)g(to)h (Ms.)g(Sarah)e(Fliegelmann)h(and)h(Mrs.)f(Carol)f(W)-7 b(ein)n(traub,)29 b(who)f(had)515 623 y(main)n(tained)19 b(and)g(up)r(dated)h(the)g(bibliograph)n(y-\014le,)f(exp)r(ertly)g(and) g(skilfully)-7 b(,)21 b(o)n(v)n(er)d(sev)n(eral)515 722 y(di\013eren)n(t)26 b(T)887 740 y(E)933 722 y(X)g(generations)e(in)i (the)g(past,)f(to)h(Silvio)f(Levy)-7 b(,)26 b(who)f(has)h(edited)g(and) f(trans-)515 822 y(formed)h(it)h(in)n(to)f(L)1064 805 y Fd(A)1101 822 y Fj(T)1147 840 y(E)1193 822 y(X2e)g(in)h(1996,)e(and)h (to)g(W)-7 b(olfgang)26 b(Slan)n(y)-7 b(,)26 b(who)g(has)g(transformed) g(it)515 922 y(in)n(to)h(a)g(BIBT)-7 b(eX)28 b(\014le)g(at)f(the)h(end) g(of)f(the)h(previous)f(millenium.)515 1204 y Fk(10)135 b(The)44 b(Bibliograph)l(y)598 1395 y Fj(1.)d(B.)30 b(Abramson)f(and)h (M.)h(Y)-7 b(ung)30 b([1989],)f(Divide)h(and)g(conquer)g(under)g (global)f(con-)704 1494 y(strain)n(ts:)f(a)g(solution)h(to)f(the)h Fe(n)p Fj(-queens)f(problem,)h Fi(J.)i(Par)l(al)t(lel)i(Distrib.)e (Comput.)704 1594 y Fc(6)p Fj(,)c(649{662.)598 1702 y(2.)41 b(A.)28 b(Adac)n(hi,)g(S.)g(Iw)n(ata)f(and)h(T.)g(Kasai)f([1981],)f(Lo) n(w)h(lev)n(el)h(complexit)n(y)f(for)h(com)n(bi-)704 1801 y(natorial)g(games,)g Fi(Pr)l(o)l(c.)k(13th)h(A)n(nn.)d(A)n(CM)i (Symp.)g(The)l(ory)h(of)f(Computing)g(\(Mil-)704 1901 y(wauke)l(e,)e(WI,)h(1981\))s Fj(,)e(Asso)r(c.)e(Comput.)h(Mac)n(h.,)f (New)h(Y)-7 b(ork,)27 b(NY,)h(pp.)g(228{237.)598 2009 y(3.)41 b(A.)29 b(Adac)n(hi,)f(S.)g(Iw)n(ata)g(and)g(T.)g(Kasai)f ([1984],)g(Some)h(com)n(binatorial)f(game)g(prob-)704 2109 y(lems)g(require)g(\012\()p Fe(n)1315 2078 y Fb(k)1356 2109 y Fj(\))h(time,)g Fi(J.)i(Asso)l(c.)g(Comput.)g(Mach.)g Fc(31)p Fj(,)d(361{376.)598 2216 y(4.)41 b(H.)22 b(Adac)n(hi,)h(H.)f (Kamek)-5 b(a)n(w)n(a)20 b(and)i(S.)h(Iw)n(ata)e([1987],)g(Shogi)g(on)h Fe(n)8 b Ff(\002)g Fe(n)21 b Fj(b)r(oard)h(is)g(com-)704 2316 y(plete)28 b(in)g(exp)r(onen)n(tial)f(time,)h Fi(T)-6 b(r)l(ans.)30 b(IEICE)39 b Fc(J70-D)p Fj(,)27 b(1843{1852)d(\(in)k (Jpanese\).)598 2424 y(5.)41 b(W.)21 b(Ahrens)g([1910],)e Fi(Mathematische)25 b(Unterhaltungen)e(und)g(Spiele)6 b Fj(,)22 b(V)-7 b(ol.)21 b(I,)g(T)-7 b(eub-)704 2524 y(ner,)27 b(Leipzig,)g(Zw)n(eite)h(v)n(ermehrte)e(und)i(v)n(erb)r (esserte)e(Au\015age.)598 2632 y(6.)41 b(M.)e(Aigner)f([1996],)f(Searc) n(hing)g(with)j(lies,)e Fi(J.)i(Combin.)i(The)l(ory)48 b Fj(\(Ser.)39 b(A\))g Fc(74)p Fj(,)704 2731 y(43{56.)598 2839 y(7.)i(M.)31 b(Aigner)f(and)h(M.)g(F)-7 b(romme)30 b([1984],)g(A)h(game)f(of)g(cops)h(and)f(robb)r(ers,)g Fi(Discr)l(ete)704 2939 y(Appl.)h(Math.)e Fc(8)p Fj(,)e(1{12.)598 3047 y(8.)41 b(M.)26 b(Ajtai,)h(L.)f(Csirmaz)f(and)h(Z.)g(Nagy)f ([1979],)f(On)i(a)f(generalization)g(of)g(the)i(game)704 3146 y(Go-Moku)f(I,)i Fi(Studia)i(Sci.)g(Math.)i(Hungar.)27 b Fc(14)p Fj(,)g(209{226.)598 3254 y(9.)41 b(E.)34 b(Akin)i(and)e(M.)h (Da)n(vis)g([1985],)e(Bulgarian)g(solitaire,)h Fi(A)n(mer.)i(Math.)i (Monthly)704 3354 y Fc(92)p Fj(,)27 b(237{250.)556 3462 y(10.)41 b(R.)26 b(E.)g(Allardice)g(and)f(A.)i(Y.)g(F)-7 b(raser)24 b([1884],)h(La)g(tour)h(d'Hano)-9 b(\177)-32 b(\020,)25 b Fi(Pr)l(o)l(c.)k(Edinbur)l(gh)704 3561 y(Math.)i(So)l(c.)d Fc(2)p Fj(,)g(50{53.)556 3669 y(11.)41 b(D.)g(T.)g(Allemang)g([1984],)e (Mac)n(hine)i(computation)g(with)g(\014nite)h(games,)e(M.Sc.)704 3769 y(Thesis,)27 b(Cam)n(bridge)f(Univ)n(ersit)n(y)-7 b(.)556 3877 y(12.)41 b(J.)h(D.)g(Allen)g([1989],)f(A)h(note)f(on)h (the)g(computer)g(solution)f(of)h(Connect-F)-7 b(our,)704 3977 y Fi(Heuristic)39 b(Pr)l(o)l(gr)l(amming)h(in)f(A)n(rti\014cial)h (Intel)t(ligenc)l(e)46 b Fj(1:)38 b Fi(The)i(First)f(Computer)704 4076 y(Olympiad)33 b Fj(\(D.)24 b(N.)g(L.)f(Levy)f(and)h(D.)g(F.)h (Beal,)e(eds.\),)h(Ellis)g(Horw)n(o)r(o)r(d,)f(Chic)n(hester,)704 4176 y(England,)27 b(pp.)h(134{135.)556 4284 y(13.)41 b(L.)35 b(V.)h(Allis)g([1994],)e(Searc)n(hing)g(for)g(solutions)h(in)h (games)e(and)i(arti\014cial)e(in)n(telli-)704 4383 y(gence,)27 b(Ph.D.)h(Thesis,)f(Univ)n(ersit)n(y)g(of)g(Lim)n(burg.)704 4483 y(ftp://ftp.cs.vu.nl/pub/victor/PhDthesis/thesis.ps.Z)556 4591 y(14.)41 b(L.)k(V.)g(Allis)g(and)g(P)-7 b(.)45 b(N.)g(A.)h(Sc)n (ho)r(o)e([1992],)f(Qubic)i(solv)n(ed)f(again,)g Fi(Heuristic)704 4691 y(Pr)l(o)l(gr)l(amming)35 b(in)f(A)n(rti\014cial)g(Intel)t(ligenc) l(e)41 b Fj(3:)34 b Fi(The)h(Thir)l(d)h(Computer)e(Olympiad)704 4790 y Fj(\(H.)k(J.)f(v)-5 b(an)37 b(den)h(Herik)f(and)g(L.)g(V.)h (Allis,)f(eds.\),)h(Ellis)f(Horw)n(o)r(o)r(d,)f(Chic)n(hester,)704 4890 y(England,)27 b(pp.)h(192{204.)p eop %%Page: 8 8 8 7 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina)-6 b(torics)32 b(#DS2)791 b Fj(8)556 523 y(15.)41 b(L.)30 b(V.)h(Allis,)g(H.)g(J.)f(v)-5 b(an)31 b(den)g(Herik)f(and)g(M.)h(P)-7 b(.)30 b(H.)h(Hun)n(tjens)g([1993],)e(Go-Moku)704 623 y(solv)n(ed)c(b)n(y)g(new)i(searc)n(h)d(tec)n(hniques,)i Fi(Pr)l(o)l(c.)j(1993)h(AAAI)d(F)-6 b(al)t(l)29 b(Symp.)h(on)e(Games:) 704 722 y(Planning)k(and)g(L)l(e)l(arning)7 b Fj(,)30 b(AAAI)g(Press)e(T)-7 b(ec)n(h.)29 b(Rep)r(ort)g(FS93{02,)f(Menlo)h(P)n (ark,)704 822 y(CA,)f(pp.)g(1{9.)556 930 y(16.)41 b(J.-P)-7 b(.)25 b(Allouc)n(he,)i(D.)g(Asto)r(orian,)e(J.)i(Randall)f(and)g(J.)g (Shallit)h([1994],)e(Morphisms,)704 1029 y(squarefree)31 b(strings,)h(and)h(the)h(to)n(w)n(er)d(of)i(Hanoi)g(puzzle,)g Fi(A)n(mer.)i(Math.)h(Monthly)704 1129 y Fc(101)p Fj(,)27 b(651{658.)556 1237 y(17.)41 b(S.)27 b(Alp)r(ern)h(and)f(A.)h(Bec)n(k)f ([1991],)e(Hex)j(games)e(and)h(t)n(wist)h(maps)f(on)g(the)g(ann)n (ulus,)704 1337 y Fi(A)n(mer.)j(Math.)h(Monthly)36 b Fc(98)p Fj(,)27 b(803{811.)556 1445 y(18.)41 b(I.)31 b(Alth\177)-42 b(ofer)32 b([1988],)e(Nim)i(games)e(with)i(arbitrary)e (p)r(erio)r(dic)h(mo)n(ving)g(orders,)f Fi(In-)704 1544 y(ternat.)f(J.)h(Game)h(The)l(ory)36 b Fc(17)p Fj(,)27 b(165{175.)556 1652 y(19.)41 b(I.)35 b(Alth\177)-42 b(ofer)34 b([1988],)f(On)h(the)h(complexit)n(y)f(of)h(searc)n(hing)e(game)g (trees)h(and)h(other)704 1752 y(recursion)26 b(trees,)h Fi(J.)j(A)n(lgorithms)35 b Fc(9)p Fj(,)27 b(538{567.)556 1860 y(20.)41 b(I.)g(Alth\177)-42 b(ofer)41 b([1989],)e(Generalized)h (minimax)h(algorithms)e(are)h(no)h(b)r(etter)g(error)704 1959 y(correctors)26 b(than)i(minimax)g(is)h(itself,)g(in:)f Fi(A)l(dvanc)l(es)j(in)f(Computer)h(Chess)37 b Fj(\(D.)29 b(F.)704 2059 y(Beal,)e(ed.\),)h(V)-7 b(ol.)28 b(5,)f(Elsevier,)f (Amsterdam,)i(pp.)g(265{282.)556 2167 y(21.)41 b(I.)30 b(Alth\177)-42 b(ofer)30 b(and)g(J.)g(B)r(\177)-44 b(ultermann)30 b([1995],)f(Sup)r(erlinear)g(p)r(erio)r(d)h(lengths)g(in)h(some)704 2267 y(subtraction)c(games,)f Fi(The)l(or)l(et.)31 b(Comput.)g(Sci.)f Fj(\(Math)e(Games\))g Fc(148)p Fj(,)f(111{119.)556 2374 y(22.)41 b(M.)26 b(Anderson)f(and)h(F.)g(Harary)e([1987],)h(Ac)n(hiev)n (emen)n(t)g(and)h(a)n(v)n(oidance)e(games)h(for)704 2474 y(generating)h(ab)r(elian)h(groups,)g Fi(Internat.)i(J.)h(Game)g(The)l (ory)37 b Fc(16)p Fj(,)27 b(321{325.)556 2582 y(23.)41 b(R.)30 b(Anderson,)f(L.)h(Lo)n(v\023)-42 b(asz,)28 b(P)-7 b(.)29 b(Shor,)g(J.)h(Sp)r(encer,)f(E.)h(T)-7 b(ard\023)-42 b(os)28 b(and)h(S.)h(Winograd)704 2682 y([1989],)37 b(Disks,)i(balls)g (and)g(w)n(alls:)f(analysis)g(of)h(a)g(com)n(binatorial)e(game,)i Fi(A)n(mer.)704 2781 y(Math.)31 b(Monthly)36 b Fc(96)p Fj(,)27 b(481{493.)556 2889 y(24.)41 b(T.)e(Andreae)f([1984],)e(Note)j (on)f(a)g(pursuit)h(game)f(pla)n(y)n(ed)f(on)i(graphs,)e Fi(Discr)l(ete)704 2989 y(Appl.)31 b(Math.)e Fc(9)p Fj(,)e(111{115.)556 3097 y(25.)41 b(T.)25 b(Andreae)g([1986],)f(On)h(a)g(pursuit)g(game)f (pla)n(y)n(ed)h(on)g(graphs)f(for)g(whic)n(h)i(a)f(minor)704 3196 y(is)i(excluded,)h Fi(J.)i(Combin.)h(The)l(ory)39 b Fj(\(Ser.)27 b(B\))h Fc(41)p Fj(,)f(37{47.)556 3304 y(26.)41 b(T.)30 b(Andreae,)g(F.)h(Hartenstein)f(and)g(A.)g(W)-7 b(olter)30 b([1999],)f(A)i(t)n(w)n(o-p)r(erson)d(game)h(on)704 3404 y(graphs)35 b(where)i(eac)n(h)f(pla)n(y)n(er)f(tries)i(to)g (encircle)f(his)h(opp)r(onen)n(t's)f(men,)i Fi(The)l(or)l(et.)704 3504 y(Comput.)30 b(Sci.)h Fj(\(Math)d(Games\))f Fc(215)p Fj(,)g(305{323.)556 3611 y(27.)41 b(R.)22 b(P)-7 b(.)21 b(Anstee)h(and)g(M.)g(F)-7 b(arb)r(er)21 b([1988],)f(On)h(bridged)g (graphs)g(and)g(cop-win)g(graphs,)704 3711 y Fi(J.)30 b(Combin.)h(The)l(ory)38 b Fj(\(Ser.)28 b(B\))g Fc(44)p Fj(,)f(22{28.)556 3819 y(28.)41 b(A.)32 b(F.)g(Arc)n(her)f([1999],)f(A) j(mo)r(dern)e(treatmen)n(t)h(of)g(the)g(15)f(puzzle,)h Fi(A)n(mer.)i(Math.)704 3919 y(Monthly)i Fc(106)p Fj(,)27 b(793{799.)556 4027 y(29.)41 b(M.)33 b(Asc)n(her)f([1987],)f(Mu)i(T)-7 b(orere:)31 b(An)j(analysis)d(of)i(a)f(Maori)g(game,)g Fi(Math.)j(Mag.)704 4126 y Fc(60)p Fj(,)27 b(90{100.)556 4234 y(30.)41 b(I.)36 b(M.)g(Asel'dero)n(v)-5 b(a)35 b([1974],)f(On)h(a)h(certain)f(discrete)h(pursuit)g(game)f(on)g (graphs,)704 4334 y Fi(Cyb)l(ernetics)g Fc(10)p Fj(,)27 b(859{864,)e(trans.)i(of)g Fi(Kib)l(ernetika)i Fc(10)e Fj(\(1974\))f(102{105.)556 4442 y(31.)41 b(J.)21 b(A.)h(Aslam)f(and)g (A.)h(Dhagat)f([1993],)e(On-line)i(algorithms)f(for)h(2-coloring)e(h)n (yp)r(er-)704 4541 y(graphs)f(via)g(c)n(hip)h(games,)f Fi(The)l(or)l(et.)23 b(Comput.)g(Sci.)g Fj(\(Math)c(Games\))g Fc(112)p Fj(,)f(355{369.)556 4649 y(32.)41 b(M.)28 b(D.)h(A)n(tkinson)f ([1981],)f(The)i(cyclic)f(to)n(w)n(ers)e(of)j(Hanoi,)f Fi(Inform.)j(Pr)l(o)l(c)l(ess.)g(L)l(ett.)704 4749 y Fc(13)p Fj(,)c(118{119.)556 4857 y(33.)41 b(J.)33 b(M.)g(Auger)g ([1991],)e(An)j(in\014ltration)f(game)f(on)h Fe(k)j Fj(arcs,)c Fi(Naval)j(R)l(es.)g(L)l(o)l(gistics)704 4956 y Fc(38)p Fj(,)27 b(511{529.)p eop %%Page: 9 9 9 8 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina)-6 b(torics)32 b(#DS2)791 b Fj(9)556 523 y(34.)41 b(R.)c(Austin)h([1976],) e(Impartial)h(and)g(partisan)f(games,)h(M.Sc.)g(Thesis,)g(Univ.)h(of) 704 623 y(Calgary)-7 b(.)556 731 y(35.)41 b(J.)19 b(O.)g(A.)g(Ay)n(eni) g(and)g(H.)h(O.)f(D.)h(Longe)e([1985],)f(Game)i(p)r(eople)g(pla)n(y:)g (Ay)n(o,)f Fi(Internat.)704 830 y(J.)30 b(Game)g(The)l(ory)37 b Fc(14)p Fj(,)27 b(207{218.)556 938 y(36.)41 b(L.)29 b(Babai)f(and)g(S.)h(Moran)f([1988],)f(Arth)n(ur{Merlin)h(games:)f(a)i (randomized)f(pro)r(of)704 1038 y(system,)d(and)g(a)g(hierarc)n(h)n(y)e (of)i(complexit)n(y)g(classes,)f Fi(J.)k(Comput.)g(System)f(Sci.)f Fc(36)p Fj(,)704 1137 y(254{276.)556 1245 y(37.)41 b(R.)35 b(J.)f(R.)h(Bac)n(k)e(and)i(J.)f(v)n(on)g(W)-7 b(righ)n(t)34 b([1995],)f(Games)h(and)h(winning)f(strategies,)704 1345 y Fi(Inform.)c(Pr)l(o)l(c)l(ess.)h(L)l(ett.)c Fc(53)p Fj(,)g(165{172.)556 1453 y(38.)41 b(C.)33 b(K.)g(Bailey)f(and)h(M.)h (E.)e(Kidw)n(ell)h([1985],)e(A)j(king's)e(tour)h(of)g(the)h(c)n(hessb)r (oard,)704 1553 y Fi(Math.)d(Mag.)e Fc(58)p Fj(,)e(285{286.)556 1660 y(39.)41 b(W.)24 b(W.)h(R.)f(Ball)g(and)g(H.)g(S.)g(M.)h(Co)n (xeter)d([1987],)h Fi(Mathematic)l(al)28 b(R)l(e)l(cr)l(e)l(ations)e (and)704 1760 y(Essays)7 b Fj(,)28 b(Do)n(v)n(er,)f(New)g(Y)-7 b(ork,)27 b(NY,)i(13th)e(edn.)556 1868 y(40.)41 b(B.)21 b(Banasc)n(hewski)f(and)h(A.)h(Pultr)f([1990/91],)d(T)-7 b(arski's)20 b(\014xp)r(oin)n(t)i(lemma)f(and)h(com-)704 1968 y(binatorial)k(games,)h Fi(Or)l(der)37 b Fc(7)p Fj(,)27 b(375{386.)556 2076 y(41.)41 b(R.)31 b(B.)h(Banerji)e([1971],)g (Similarities)h(in)g(games)g(and)g(their)g(use)g(in)h(strategy)e(con-) 704 2175 y(struction,)21 b Fi(Pr)l(o)l(c.)j(Symp.)h(Computers)f(and)h (A)n(utomata)i Fj(\(J.)21 b(F)-7 b(o)n(x,)21 b(ed.\),)g(P)n(olytec)n (hnic)704 2275 y(Press,)26 b(Bro)r(oklyn,)g(NY,)i(pp.)g(337{357.)556 2383 y(42.)41 b(R.)26 b(B.)h(Banerji)e([1980],)g Fi(A)n(rti\014cial)k (Intel)t(ligenc)l(e,)h(A)e(The)l(or)l(etic)l(al)j(Appr)l(o)l(ach)6 b Fj(,)28 b(Else-)704 2482 y(vier,)f(North-Holland,)g(New)g(Y)-7 b(ork,)27 b(NY.)556 2590 y(43.)41 b(R.)36 b(B.)f(Banerji)g(and)g(C.)h (A.)g(Dunning)g([1992],)d(On)j(misere)f(games,)f Fi(Cyb)l(ernetics)704 2690 y(and)c(Systems)k Fc(23)p Fj(,)27 b(221{228.)556 2798 y(44.)41 b(R.)28 b(B.)g(Banerji)f(and)h(G.)g(W.)h(Ernst)e([1972],) f(Strategy)h(construction)g(using)h(homo-)704 2897 y(morphisms)f(b)r (et)n(w)n(een)g(games,)g Fi(A)n(rti\014cial)j(Intel)t(ligenc)l(e)35 b Fc(3)p Fj(,)27 b(223{249.)556 3005 y(45.)41 b(R.)26 b(Bar)f(Y)-7 b(eh)n(uda,)26 b(T.)g(Etzion)g(and)g(S.)g(Moran)f([1993],) f(Rotating-table)h(games)g(and)704 3105 y(deriv)-5 b(ativ)n(es)26 b(of)i(w)n(ords,)e Fi(The)l(or)l(et.)31 b(Comput.)g(Sci.)f Fj(\(Math)e(Games\))f Fc(108)p Fj(,)g(311{329.)556 3213 y(46.)41 b(I.)47 b(B\023)-42 b(ar\023)g(an)n(y)45 b([1979],)h(On)h(a)f (class)g(of)h(balancing)g(games,)f Fi(J.)h(Combin.)i(The)l(ory)704 3313 y Fj(\(Ser.)27 b(A\))i Fc(26)p Fj(,)e(115{126.)556 3421 y(47.)41 b(J.)26 b(G.)h(Baron)e([1974],)g(The)h(game)g(of)h(nim)g (|)f(a)g(heuristic)h(approac)n(h,)d Fi(Math.)30 b(Mag.)704 3520 y Fc(47)p Fj(,)d(23{28.)556 3628 y(48.)41 b(R.)28 b(Barua)f(and)h(S.)h(Ramakrishnan)d([1996],)h Fe(\033)s Fj(-game,)g Fe(\033)2510 3598 y Fd(+)2566 3628 y Fj(-game)g(and)h(t)n (w)n(o-dimen-)704 3728 y(sional)35 b(additiv)n(e)h(cellular)f (automata,)g Fi(The)l(or)l(et.)j(Comput.)h(Sci.)f Fj(\(Math)e(Games\)) 704 3827 y Fc(154)p Fj(,)27 b(349{366.)556 3935 y(49.)41 b(V.)30 b(J.)g(D.)g(Baston)f(and)g(F.)h(A.)h(Bosto)r(c)n(k)d([1985],)g (A)i(game)f(lo)r(cating)g(a)h(needle)f(in)h(a)704 4035 y(cirular)c(ha)n(ystac)n(k,)g Fi(J.)k(Optimization)h(The)l(ory)g(and)f (Applic)l(ations)36 b Fc(47)p Fj(,)27 b(383{391.)556 4143 y(50.)41 b(V.)30 b(J.)g(D.)g(Baston)f(and)g(F.)h(A.)h(Bosto)r(c)n (k)d([1986],)g(A)i(game)f(lo)r(cating)g(a)h(needle)f(in)h(a)704 4242 y(square)c(ha)n(ystac)n(k,)g Fi(J.)k(Optimization)g(The)l(ory)i (and)e(Applic)l(ations)36 b Fc(51)p Fj(,)27 b(405{419.)556 4350 y(51.)41 b(V.)30 b(J.)g(D.)h(Baston)e(and)h(F.)g(A.)h(Bosto)r(c)n (k)d([1987],)h(Discrete)g(hamstrung)h(squad)f(car)704 4450 y(games,)d Fi(Internat.)k(J.)g(Game)g(The)l(ory)37 b Fc(16)p Fj(,)27 b(253{261.)556 4558 y(52.)41 b(V.)25 b(J.)g(D.)h(Baston)e(and)h(F.)g(A.)h(Bosto)r(c)n(k)d([1988],)h(A)h (simple)g(co)n(v)n(er-up)f(game,)g Fi(A)n(mer.)704 4658 y(Math.)31 b(Monthly)36 b Fc(95)p Fj(,)27 b(850{854.)556 4765 y(53.)41 b(V.)31 b(J.)f(D.)i(Baston)d(and)i(F.)g(A.)g(Bosto)r(c)n (k)f([1989],)f(A)i(one-dimensional)e(helicopter-)704 4865 y(submarine)e(game,)g Fi(Naval)j(R)l(es.)g(L)l(o)l(gistics)35 b Fc(36)p Fj(,)27 b(479{490.)p eop %%Page: 10 10 10 9 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(10)556 523 y(54.)41 b(V.)28 b(J.)f(D.)h(Baston)e(and)h(F.)h(A.)g(Bosto)r(c)n(k)d([1993],)h (In\014nite)i(deterministic)g(graphical)704 623 y(games,)e Fi(SIAM)k(J.)g(Contr)l(ol)g(Optim.)e Fc(31)p Fj(,)f(1623{1629.)556 731 y(55.)41 b(J.)28 b(Baumgartner,)e(F.)j(Galvin,)f(R.)h(La)n(v)n(er)d (and)i(R.)h(McKenzie)e([1975],)g(Game)h(the-)704 830 y(oretic)f(v)n(ersions)f(of)i(partition)g(relations,)f(in:)h Fi(Col)t(lo)l(quia)k(Mathematic)l(a)g(So)l(cietatis)704 930 y(J\023)-42 b(anos)23 b(Bolyai)i Fc(10)p Fi(,)e(Pr)l(o)l(c.)h (Internat.)f(Col)t(lo)l(q.)i(on)e(In\014nite)f(and)i(Finite)f(Sets,)g Fj(V)-7 b(ol.)20 b(1,)704 1029 y(Keszthely)-7 b(,)22 b(Hungary)-7 b(,)21 b(1973)f(\(A.)j(Ha)5 b(jnal,)22 b(R.)h(Rado)e(and)h (V.)h(T.)f(S\023)-42 b(os,)22 b(eds.\),)h(North-)704 1129 y(Holland,)k(pp.)h(131{135.)556 1237 y(56.)41 b(J.)30 b(D.)h(Beasley)e([1985],)g Fi(The)k(Ins)f(&)g(Outs)f(of)i(Pe)l(g)g (Solitair)l(e)6 b Fj(,)32 b(Oxford)d(Univ)n(ersit)n(y)704 1337 y(Press,)d(Oxford.)556 1445 y(57.)41 b(J.)22 b(D.)g(Beasley)f ([1990],)f Fi(The)26 b(Mathematics)g(of)g(Games)7 b Fj(,)22 b(Oxford)f(Univ)n(ersit)n(y)h(Press,)704 1544 y(Oxford.)556 1652 y(58.)41 b(A.)29 b(Bec)n(k)e([1969],)g(Games,)g(in:)i Fi(Excursions)h(into)h(Mathematics)37 b Fj(\(A.)29 b(Bec)n(k,)e(M.)i (N.)704 1752 y(Bleic)n(her)d(and)i(D.)g(W.)g(Cro)n(w)n(e,)e(eds.\),)i (W)-7 b(orth)27 b(Publ.,)h(Chap.)g(5,)f(pp.)h(317{387.)556 1860 y(59.)41 b(J.)24 b(Bec)n(k)h([1981],)e(On)h(p)r(ositional)g (games,)g Fi(J.)k(Combin.)g(The)l(ory)36 b Fj(\(Ser.)25 b(A\))h Fc(30)p Fj(,)e(117{)704 1959 y(133.)556 2067 y(60.)41 b(J.)27 b(Bec)n(k)f([1981],)f(V)-7 b(an)27 b(der)g(W)-7 b(aerden)26 b(and)h(Ramsey)f(t)n(yp)r(e)i(games,)e Fi(Combinatoric)l(a) 704 2167 y Fc(1)p Fj(,)h(103{116.)556 2275 y(61.)41 b(J.)31 b(Bec)n(k)g([1982],)f(On)i(a)f(generalization)f(of)h(Kaplansky's)f (game,)h Fi(Discr)l(ete)j(Math.)704 2374 y Fc(42)p Fj(,)27 b(27{35.)556 2482 y(62.)41 b(J.)d(Bec)n(k)g([1982],)f(Remarks)g(on)h(p) r(ositional)g(games,)g(I,)g Fi(A)l(cta)i(Math.)h(A)l(c)l(ad.)f(Sci.)704 2582 y(Hungar.)28 b Fc(40)p Fj(\(1{2\),)e(65{71.)556 2690 y(63.)41 b(J.)32 b(Bec)n(k)f([1983],)g(Biased)g(Ramsey)g(t)n(yp)r (e)i(games,)e Fi(Studia)j(Sci.)g(Math.)i(Hung.)31 b Fc(18)p Fj(,)704 2790 y(287{292.)556 2897 y(64.)41 b(J.)g(Bec)n(k)h([1985],)e (Random)h(graphs)g(and)g(p)r(ositional)h(games)e(on)i(the)g(complete) 704 2997 y(graph,)26 b Fi(A)n(nn.)j(Discr)l(ete)h(Math.)f Fc(28)p Fj(,)e(7{13.)556 3105 y(65.)41 b(J.)30 b(Bec)n(k)f([1997],)f (Games,)i(randomness)f(and)g(algorithms,)g(in:)h Fi(The)j(Mathematics) 704 3205 y(of)h(Paul)f(Er)l(d})-42 b(os)39 b Fj(\(R.)31 b(L.)g(Graham)f(and)h(J.)g(Ne)l(\024)-37 b(set)l(\024)g(ril,)28 b(eds.\),)k(V)-7 b(ol.)31 b(I,)g(Springer,)f(pp.)704 3304 y(280{310.)556 3412 y(66.)41 b(J.)e(Bec)n(k)g([1997],)e(Graph)i (games,)g Fi(Pr)l(o)l(c.)i(Int.)f(Col)t(l.)j(Extr)l(emal)d(Gr)l(aph)i (The)l(ory)7 b Fj(,)704 3512 y(Balatonlelle,)26 b(Hungary)-7 b(.)556 3620 y(67.)41 b(J.)29 b(Bec)n(k)f(and)i(L.)f(Csirmaz)f([1982],) g(V)-7 b(ariations)28 b(on)h(a)g(game,)f Fi(J.)k(Combin.)g(The)l(ory) 704 3719 y Fj(\(Ser.)27 b(A\))i Fc(33)p Fj(,)e(297{315.)556 3827 y(68.)41 b(R.)34 b(Beigel)g(and)g(W.)g(I.)g(Gasarc)n(h)f([1991],)f (The)i(mapmak)n(er's)f(dilemma,)h Fi(Discr)l(ete)704 3927 y(Appl.)d(Math.)e Fc(34)p Fj(,)e(37{48.)556 4035 y(69.)41 b(R.)28 b(C.)f(Bell)h([1960,)d(1969],)h Fi(Bo)l(ar)l(d)31 b(and)f(T)-6 b(able)31 b(Games)7 b Fj(,)28 b(V)-7 b(ol.)28 b(I)f(&)g(I)r(I,)h(Oxford)f(Uni-)704 4134 y(v)n(ersit)n(y)f(Press.)556 4242 y(70.)41 b(R.)i(Bell)g([1988],)f Fi(Bo)l(ar)l(d)j(Games)g(R)l (ound)e(the)h(World)9 b Fj(,)44 b(Cam)n(bridge)e(Univ)n(ersit)n(y)704 4342 y(Press,)26 b(Cam)n(bridge)g(\(Third)i(Prin)n(ting:)f(1993\).)556 4450 y(71.)41 b(S.)31 b(J.)h(Benk)n(oski,)d(M.)j(G.)g(Mon)n(ticino)e (and)i(J.)f(R.)g(W)-7 b(eisinger)31 b([1991],)e(A)j(surv)n(ey)e(of)704 4550 y(the)e(searc)n(h)e(theory)h(literature,)g Fi(Naval)j(R)l(es.)g(L) l(o)l(gistics)35 b Fc(38)p Fj(,)27 b(469{494.)556 4658 y(72.)41 b(G.)28 b(Bennett)h([1994],)e(Double)h(dipping:)h(the)f(case)g (of)g(the)h(missing)e(binomial)h(co)r(ef-)704 4757 y(\014cien)n(t)g (iden)n(tities,)g Fi(The)l(or)l(et.)i(Comput.)h(Sci.)f Fj(\(Math)e(Games\))g Fc(123)p Fj(,)f(351{375.)556 4865 y(73.)41 b(D.)26 b(Berengut)f([1981],)f(A)i(random)f(hopscotc)n(h)f (problem)i(or)e(ho)n(w)i(to)f(mak)n(e)g(Johnn)n(y)704 4965 y(read)20 b(more,)g(in:)h Fi(The)j(Mathematic)l(al)i(Gar)l(dner)k Fj(\(D.)22 b(A.)f(Klarner,)e(ed.\),)i(W)-7 b(adsw)n(orth)p eop %%Page: 11 11 11 10 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(11)704 523 y(In)n(ternat.,)27 b(Belmon)n(t,)g(CA,)h(pp.)g(51{59.)556 631 y(74.)41 b(B.)g(Berezo)n (vskiy)d(and)i(A.)h(Gnedin)h([1984],)d(The)i(b)r(est)g(c)n(hoice)f (problem,)g Fi(A)n(kad.)704 731 y(Nauk,)30 b(USSR,)f(Mosc)l(ow)40 b Fj(\(in)28 b(Russian\))f(.)556 839 y(75.)41 b(C.)25 b(Berge)f([1976],)f(Sur)i(les)g(jeux)h(p)r(ositionnels,)e Fi(Cahiers)30 b(du)d(Centr)l(e)2924 818 y(\023)2912 839 y(Etudes)h(R)l(e)l(ch.)704 938 y(Op)n(\023)-40 b(er.)28 b Fc(18)p Fj(,)f(91{107.)556 1046 y(76.)41 b(C.)26 b(Berge)f([1977],)g (V)-7 b(ers)26 b(une)h(th)n(\023)-39 b(eorie)25 b(g)n(\023)-39 b(en)n(\023)g(erale)23 b(des)j(jeux)h(p)r(ositionnels,)f(in:)g Fi(Math-)704 1146 y(ematic)l(al)h(Ec)l(onomics)h(and)e(Game)h(The)l (ory,)i(Essays)e(in)f(honor)h(of)g(Oskar)g(Mor)l(gen-)704 1245 y(stern,)g Fj(Lecture)f(Notes)f(in)h(Economics)e(\(R.)i(Henn)g (and)f(O.)g(Mo)r(esc)n(hlin,)g(eds.\),)h(V)-7 b(ol.)704 1345 y(141,)26 b(Springer)h(V)-7 b(erlag,)26 b(Berlin,)h(pp.)h(13{24.) 556 1453 y(77.)41 b(C.)21 b(Berge)f([1981],)f(Some)i(remarks)f(ab)r (out)h(a)g(Hex)g(problem,)g(in:)g Fi(The)k(Mathematic)l(al)704 1553 y(Gar)l(dner)33 b Fj(\(D.)25 b(A.)f(Klarner,)d(ed.\),)k(W)-7 b(adsw)n(orth)22 b(In)n(ternat.,)h(Belmon)n(t,)h(CA,)g(pp.)f(25{)704 1652 y(27.)556 1760 y(78.)41 b(C.)28 b(Berge)e([1985],)g Fi(Gr)l(aphs)7 b Fj(,)29 b(North-Holland,)d(Amsterdam,)i(Chap.)f(14.) 556 1868 y(79.)41 b(C.)e(Berge)f([1989],)f Fi(Hyp)l(er)l(gr)l(aphs)7 b Fj(,)41 b(Elsevier)c(\(F)-7 b(renc)n(h:)39 b(Gauthier)g(Villars)g (1988\),)704 1968 y(Chap.)27 b(4.)556 2076 y(80.)41 b(C.)c(Berge)f ([1996],)g(Com)n(binatorial)g(games)g(on)h(a)g(graph,)f Fi(Discr)l(ete)j(Math.)g Fc(151)p Fj(,)704 2175 y(59{65.)556 2283 y(81.)i(C.)f(Berge)f(and)g(P)-7 b(.)40 b(Duc)n(het)h([1988],)d(P)n (erfect)h(graphs)f(and)i(k)n(ernels,)f Fi(Bul)t(l.)j(Inst.)704 2383 y(Math.)31 b(A)l(c)l(ad.)f(Sinic)l(a)35 b Fc(16)p Fj(,)27 b(263{274.)556 2491 y(82.)41 b(C.)25 b(Berge)f(and)h(P)-7 b(.)25 b(Duc)n(het)h([1990],)e(Recen)n(t)h(problems)f(and)h(results)g (ab)r(out)g(k)n(ernels)704 2590 y(in)j(directed)f(graphs,)f Fi(Discr)l(ete)k(Math.)f Fc(86)p Fj(,)e(27{31.)556 2698 y(83.)41 b(C.)46 b(Berge)f(and)h(M.)h(Las)e(V)-7 b(ergnas)45 b([1976],)g(Un)i(nouv)n(eau)e(jeu)i(p)r(ositionnel,)f(le)704 2798 y(\\Matc)n(h-It",)18 b(ou)h(une)h(construction)f(dialectique)g (des)g(couplages)f(parfaits,)h Fi(Cahiers)704 2897 y(du)30 b(Centr)l(e)1103 2876 y(\023)1091 2897 y(Etudes)g(R)l(e)l(ch.)g(Op)n (\023)-40 b(er.)28 b Fc(18)p Fj(,)f(83{89.)556 3005 y(84.)41 b(E.)35 b(R.)g(Berlek)-5 b(amp)35 b([1972],)f(Some)h(recen)n(t)g (results)g(on)g(the)g(com)n(binatorial)f(game)704 3105 y(called)27 b(W)-7 b(elter's)28 b(Nim,)g Fi(Pr)l(o)l(c.)j(6th)f(A)n (nn.)f(Princ)l(eton)h(Conf.)h(Information)g(Scienc)l(e)704 3205 y(and)f(Systems)7 b Fj(,)27 b(pp.)h(203{204.)556 3313 y(85.)41 b(E.)24 b(R.)h(Berlek)-5 b(amp)24 b([1974],)f(The)i(Hac)n (k)n(en)n(bush)f(n)n(um)n(b)r(er)g(system)h(for)f(compresssion)704 3412 y(of)j(n)n(umerical)g(data,)g Fi(Inform.)k(and)f(Contr)l(ol)37 b Fc(26)p Fj(,)27 b(134{140.)556 3520 y(86.)41 b(E.)20 b(R.)h(Berlek)-5 b(amp)20 b([1988],)f(Blo)r(c)n(kbusting)h(and)g (domineering,)g Fi(J.)k(Combin.)g(The)l(ory)704 3620 y Fj(\(Ser.)h(A\))g Fc(49)p Fj(,)f(67{116,)e(an)j(earlier)e(v)n (ersion,)g(en)n(titled)j(In)n(tro)r(duction)e(to)h(blo)r(c)n(kbust-)704 3719 y(ing)e(and)h(domineering,)e(app)r(eared)h(in:)h Fi(The)j(Lighter)g(Side)g(of)g(Mathematics)p Fj(,)e(Pro)r(c.)704 3819 y(E.)30 b(Strens)g(Memorial)g(Conf.)g(on)h(Recr.)f(Math.)g(and)h (its)f(History)-7 b(,)30 b(Calgary)-7 b(,)29 b(1986,)704 3919 y(Sp)r(ectrum)j(Series)f(\(R.)i(K.)e(Guy)h(and)g(R.)g(E.)g(W)-7 b(o)r(o)r(dro)n(w,)31 b(eds.\),)h(Math.)g(Asso)r(c.)f(of)704 4018 y(America,)c(W)-7 b(ashington,)27 b(DC,)h(1994,)e(pp.)i(137{148.) 556 4126 y(87.)41 b(E.)29 b(Berlek)-5 b(amp)28 b([1990],)g(Tw)n(o-p)r (erson,)f(p)r(erfect-information)h(games,)h(in:)g Fi(The)j(L)l(e-)704 4226 y(gacy)i(of)h(John)e(von)h(Neumann)k Fj(\(Hempstead)32 b(NY,)h(1988\))p Fi(,)f(Pr)l(o)l(c.)i(Symp)l(os.)g(Pur)l(e)704 4325 y(Math.)p Fj(,)29 b(V)-7 b(ol.)28 b(50,)e(Amer.)i(Math.)g(So)r (c.,)f(Pro)n(vidence,)f(RI,)i(pp.)g(275{287.)556 4433 y(88.)41 b(E.)32 b(R.)h(Berlek)-5 b(amp)31 b([1991],)g(In)n(tro)r (ductory)g(o)n(v)n(erview)g(of)h(mathematical)g(Go)g(end-)704 4533 y(games,)g(in:)h Fi(Combinatorial)k(Games,)f Fj(Pro)r(c.)c(Symp.)h (Appl.)h(Math.)f(\(R.)g(K.)g(Guy)-7 b(,)704 4633 y(ed.\),)28 b(V)-7 b(ol.)28 b(43,)e(Amer.)i(Math.)g(So)r(c.,)f(Pro)n(vidence,)f (RI,)i(pp.)g(73{100.)556 4741 y(89.)41 b(E.)26 b(R.)h(Berlek)-5 b(amp)27 b([1996],)e(The)i(economist's)f(view)g(of)h(com)n(binatorial)e (games,)h(in:)704 4840 y Fi(Games)37 b(of)h(No)f(Chanc)l(e,)h Fj(Pro)r(c.)c(MSRI)i(W)-7 b(orkshop)34 b(on)h(Com)n(binatorial)e (Games,)704 4940 y(July)-7 b(,)34 b(1994,)e(Berk)n(eley)-7 b(,)33 b(CA,)i(MSRI)g(Publ.)f(\(R.)g(J.)h(No)n(w)n(ak)n(o)n(wski,)c (ed.\),)k(V)-7 b(ol.)34 b(29,)p eop %%Page: 12 12 12 11 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(12)704 523 y(Cam)n(bridge)26 b(Univ)n(ersit)n(y)h(Press,)f(Cam)n(bridge,)g(pp.)i(365{405.)556 631 y(90.)41 b(E.)27 b(R.)g(Berlek)-5 b(amp,)26 b(J.)h(H.)g(Con)n(w)n (a)n(y)f(and)g(R.)i(K.)e(Guy)i([1982],)d Fi(Winning)k(Ways)h(for)704 731 y(your)f(mathematic)l(al)h(plays)7 b Fj(,)28 b(V)-7 b(ol.)27 b(I)g(&)f(I)r(I,)h(Academic)g(Press,)e(London,)h(translated) 704 830 y(in)n(to)k(German:)g Fi(Gewinnen,)j(Str)l(ate)l(gien)f(f)q (\177)-43 b(ur)33 b(Mathematische)h(Spiele)e Fj(b)n(y)e(G.)h(Seif-)704 930 y(fert,)i(F)-7 b(orew)n(ord)30 b(b)n(y)i(K.)g(Jacobs,)f(M.)i(Rem)n (\023)-39 b(en)n(yi)31 b(and)i(Sei\013ert,)g(F)-7 b(riedr.)32 b(View)n(eg)f(&)704 1029 y(Sohn,)c(Braunsc)n(h)n(w)n(eig)e(\(four)j(v)n (olumes\),)f(1985.)556 1137 y(91.)41 b(E.)21 b(R.)i(Berlek)-5 b(amp)21 b(and)h(Y.)g(Kim)g([1996],)e(Where)i(is)g(the)h (\\Thousand-Dollar)c(Ko?",)704 1237 y(in:)j Fi(Games)k(of)f(No)g(Chanc) l(e,)h Fj(Pro)r(c.)21 b(MSRI)h(W)-7 b(orkshop)21 b(on)h(Com)n (binatorial)e(Games,)704 1337 y(July)-7 b(,)34 b(1994,)e(Berk)n(eley)-7 b(,)33 b(CA,)i(MSRI)g(Publ.)f(\(R.)g(J.)h(No)n(w)n(ak)n(o)n(wski,)c (ed.\),)k(V)-7 b(ol.)34 b(29,)704 1436 y(Cam)n(bridge)26 b(Univ)n(ersit)n(y)h(Press,)f(Cam)n(bridge,)g(pp.)i(203{226.)556 1544 y(92.)41 b(E.)31 b(Berlek)-5 b(amp)31 b(and)g(T.)h(Ro)r(dgers,)e (eds.)i([1999],)d Fi(The)35 b(Mathemagician)h(and)e(Pie)l(d)704 1644 y(Puzzler)9 b Fj(,)40 b(A.)h(K.)f(P)n(eters,)f(W)-7 b(ellesley)g(,)40 b(MA)g(02181,)e(A)j(collection)e(in)i(tribute)f(to) 704 1743 y(Martin)25 b(Gardner.)g(P)n(ap)r(ers)f(from)i(the)g (Gathering)f(for)h(Gardner)e(Meeting)i(\(G4G1\))704 1843 y(held)i(in)g(A)n(tlan)n(ta,)f(GA,)h(Jan)n(uary)e(1993.)556 1951 y(93.)41 b(E.)27 b(Berlek)-5 b(amp)27 b(and)h(D.)g(W)-7 b(olfe)28 b([1994],)f Fi(Mathematic)l(al)k(Go)g(|)f(Chil)t(ling)i(Gets) e(the)704 2051 y(L)l(ast)f(Point)8 b Fj(,)28 b(A.)g(K.)g(P)n(eters,)e (W)-7 b(ellesley)g(,)28 b(MA)g(02181.)556 2159 y(94.)41 b(P)-7 b(.)27 b(Berlo)r(quin)g([1976],)f Fi(100)31 b(Jeux)e(de)h(T)-6 b(able)6 b Fj(,)29 b(Flammarion,)d(P)n(aris.)556 2267 y(95.)41 b(N.)25 b(L.)f(Biggs)f([1999],)g(Chip-\014ring)g(and)h(the)h (critical)f(group)f(of)h(a)g(graph,)f Fi(J.)k(A)n(lgebr.)704 2366 y(Comb.)i Fc(9)p Fj(,)e(25{45.)556 2474 y(96.)41 b(J.)23 b(Bitar)g(and)h(E.)f(Goles)g([1992],)f(P)n(arallel)g(c)n(hip)h (\014ring)g(games)g(on)g(graphs,)g Fi(The)l(or)l(et.)704 2574 y(Comput.)30 b(Sci.)f Fc(92)p Fj(,)e(291{300.)556 2682 y(97.)41 b(A.)28 b(Bj\177)-42 b(orner)26 b(and)h(L.)g(Lo)n(v\023) -42 b(asz)25 b([1992],)h(Chip-\014ring)h(games)f(on)h(directed)g (graphs,)f Fi(J.)704 2781 y(A)n(lgebr)l(aic)31 b(Combin.)e Fc(1)p Fj(,)e(305{328.)556 2889 y(98.)41 b(A.)35 b(Bj\177)-42 b(orner,)34 b(L.)h(Lo)n(v\023)-42 b(asz)33 b(and)i(P)-7 b(.)34 b(Chor)g([1991],)g(Chip-\014ring)g(games)g(on)g(graphs,)704 2989 y Fi(Eur)l(op)l(e)l(an)c(J.)g(Combin.)f Fc(12)p Fj(,)e(283{291.)556 3097 y(99.)41 b(D.)30 b(Blac)n(kw)n(ell)f(and)h(M.) g(A.)g(Girshic)n(k)f([1954],)g Fi(The)l(ory)k(of)g(Games)f(and)h (Statistic)l(al)704 3196 y(De)l(cisions)7 b Fj(,)28 b(Wiley)-7 b(,)28 b(New)g(Y)-7 b(ork,)27 b(NY.)515 3304 y(100.)40 b(U.)24 b(Blass)f(and)h(A.)g(S.)g(F)-7 b(raenk)n(el)23 b([1990],)f(The)i(Sprague{Grundy)e(function)i(of)g(Wyt-)704 3404 y(ho\013)6 b('s)28 b(game,)f Fi(The)l(or)l(et.)k(Comput.)f(Sci.)h Fj(\(Math)d(Games\))f Fc(75)p Fj(,)g(311{333.)515 3512 y(101.)40 b(U.)h(Blass,)e(A.)i(S.)g(F)-7 b(raenk)n(el)39 b(and)i(R.)f(Guelman)h([1998],)e(Ho)n(w)h(far)g(can)g(Nim)h(in)704 3611 y(disguise)27 b(b)r(e)h(stretc)n(hed?,)f Fi(J.)j(Combin.)h(The)l (ory)39 b Fj(\(Ser.)27 b(A\))i Fc(84)p Fj(,)e(145{156.)515 3719 y(102.)40 b(M.)28 b(Blidia)f([1986],)f(A)i(parit)n(y)f(digraph)f (has)h(a)g(k)n(ernel,)g Fi(Combinatoric)l(a)37 b Fc(6)p Fj(,)27 b(23{27.)515 3827 y(103.)40 b(M.)31 b(Blidia,)g(P)-7 b(.)30 b(Duc)n(het,)i(H.)f(Jacob,)f(F.)h(Ma\013ra)n(y)f(and)h(H.)g (Meyniel)g([1999],)e(Some)704 3927 y(op)r(erations)j(preserving)g(the)i (existence)g(of)g(k)n(ernels,)e Fi(Discr)l(ete)k(Math.)f Fc(205)p Fj(,)e(211{)704 4027 y(216.)515 4134 y(104.)40 b(M.)28 b(Blidia,)g(P)-7 b(.)27 b(Duc)n(het)h(and)g(F.)g(Ma\013ra)n(y)f ([1993],)f(On)h(k)n(ernels)g(in)h(p)r(erfect)g(graphs,)704 4234 y Fi(Combinatoric)l(a)36 b Fc(13)p Fj(,)27 b(231{233.)515 4342 y(105.)40 b(H.)20 b(L.)g(Bo)r(dlaender)e([1991],)g(On)i(the)g (complexit)n(y)f(of)h(some)f(coloring)f(games,)g Fi(Intern.)704 4442 y(J.)30 b(F)-6 b(oundations)30 b(Computer)g(Scienc)l(e)k Fc(2)p Fj(,)28 b(133{147.)515 4550 y(106.)40 b(H.)19 b(L.)g(Bo)r(dlaender)f([1993],)g(Complexit)n(y)g(of)h(path)g(forming)g (games,)f Fi(The)l(or)l(et.)23 b(Com-)704 4649 y(put.)30 b(Sci.)g Fj(\(Math)e(Games\))g Fc(110)p Fj(,)e(215{245.)515 4757 y(107.)40 b(H.)30 b(L.)f(Bo)r(dlaender)g([1993],)f(Ka)n(yles)g(on) h(sp)r(ecial)g(classes)g(of)g(graphs|an)f(applica-)704 4857 y(tion)k(of)g(Sprague-Grundy)f(theory)-7 b(,)32 b(in:)g Fi(Gr)l(aph-the)l(or)l(etic)k(c)l(onc)l(epts)e(in)g(c)l (omputer)p eop %%Page: 13 13 13 12 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(13)704 523 y Fi(scienc)l(e)43 b Fj(\(Wiesbaden-Nauro)r(d,)33 b(1992\))p Fi(,)i Fj(Lecture)f(Notes)g (in)h(Comput.)f(Sci.,)h(V)-7 b(ol.)704 623 y(657,)26 b(Springer,)h(Berlin,)g(pp.)h(90{102.)515 731 y(108.)40 b(H.)23 b(L.)g(Bo)r(dlaender)e(and)i(D.)g(Kratsc)n(h)e([1992],)g(The)i (complexit)n(y)f(of)h(coloring)e(games)704 830 y(on)27 b(p)r(erfect)h(graphs,)e Fi(The)l(or)l(et.)31 b(Comput.)g(Sci.)f Fj(\(Math)e(Games\))g Fc(106)p Fj(,)f(309{326.)515 938 y(109.)40 b(K.)27 b(D.)h(Boklan)f([1984],)f(The)h Fe(n)p Fj(-n)n(um)n(b)r(er)g(game,)g Fi(Fib)l(onac)l(ci)32 b(Quart.)27 b Fc(22)p Fj(,)g(152{155.)515 1046 y(110.)40 b(B.)26 b(Bollob\023)-42 b(as)24 b(and)i(T.)g(Szab\023)-42 b(o)25 b([1998],)f(The)i(orien)n(ted)f(cycle)g(game,)h Fi(Discr)l(ete)i(Math.) 704 1146 y Fc(186)p Fj(,)f(55{67.)515 1254 y(111.)40 b(E.)26 b(Borel)f([1921],)g(La)h(th)n(\023)-39 b(eorie)25 b(du)h(jeu)h(et)g(les)d(\023)-39 b(equations)25 b(in)n(tegrales)g(\022) -42 b(a)26 b(no)n(y)n(au)f(sym-)704 1353 y(metrique)i(gauc)n(he,)g Fi(C.)j(R.)g(A)l(c)l(ad.)h(Sci.)f(Paris)36 b Fc(173)p Fj(,)27 b(1304{1308.)515 1461 y(112.)40 b(E.)29 b(Boros)e(and)i(V.)h (Gurevic)n(h)f([1996],)e(P)n(erfect)i(graphs)f(are)g(k)n(ernel)h(solv) -5 b(able,)28 b Fi(Dis-)704 1561 y(cr)l(ete)h(Math.)g Fc(159)p Fj(,)e(35{55.)515 1669 y(113.)40 b(E.)24 b(Boros)f(and)i(V.)g (Gurevic)n(h)f([1998],)f(A)i(corrected)f(v)n(ersion)f(of)i(the)g(Duc)n (het)g(k)n(ernel)704 1768 y(conjecture,)i Fi(Discr)l(ete)j(Math.)f Fc(179)p Fj(,)e(231{233.)515 1876 y(114.)40 b(C.)31 b(L.)f(Bouton)h ([1902],)e(Nim,)i(a)f(game)g(with)h(a)g(complete)f(mathematical)h (theory)-7 b(,)704 1976 y Fi(A)n(nn.)29 b(of)i(Math.)e Fc(3)p Fj(\(2\),)e(35{39.)515 2084 y(115.)40 b(J.)h(Bo)n(yce)f([1981],) g(A)i(Kriegspiel)e(endgame,)h(in:)h Fi(The)i(Mathematic)l(al)g(Gar)l (dner)704 2183 y Fj(\(D.)28 b(A.)g(Klarner,)e(ed.\),)i(W)-7 b(adsw)n(orth)27 b(In)n(ternat.,)g(Belmon)n(t,)g(CA,)h(pp.)g(28{36.)515 2291 y(116.)40 b(D.)d(M.)f(Breuk)n(er,)f(J.)h(W.)h(H.)f(M.)h(Uiterwijk) f(and)g(H.)h(J.)f(v)-5 b(an)36 b(den)h(Herik)f([2000],)704 2391 y(Solving)h(8)25 b Ff(\002)g Fj(8)38 b(Domineering,)g Fi(The)l(or)l(et.)j(Comput.)f(Sci.)g Fj(\(Math)f(Games\))f Fc(230)p Fj(,)704 2491 y(195{206.)515 2599 y(117.)i(D.)28 b(M.)h(Broline)e(and)h(D.)g(E.)g(Lo)r(eb)g([1995],)e(The)i(com)n (binatorics)e(of)i(Mancala-t)n(yp)r(e)704 2698 y(games:)e(Ay)n(o,)h(Tc) n(houk)-5 b(aillon,)27 b(and)g(1)p Fe(=\031)s Fj(,)h Fi(UMAP)h(J.)f Fc(16)p Fj(\(1\),)f(21{36.)515 2806 y(118.)40 b(A.)35 b(Brousseau)e([1976],)g(T)-7 b(o)n(w)n(er)33 b(of)h(Hanoi)g(with)i(more)d(p)r(egs,)i Fi(J.)h(R)l(e)l(cr.)g(Math.)g Fc(8)p Fj(,)704 2906 y(169{178.)515 3014 y(119.)k(R.)35 b(A.)g(Brualdi)f(and)g(V.)h(S.)g(Pless)f([1993],)f(Greedy)h(co)r(des,)g Fi(J.)j(Combin.)g(The)l(ory)704 3113 y Fj(\(Ser.)27 b(A\))i Fc(64)p Fj(,)e(10{30.)515 3221 y(120.)40 b(A.)32 b(A.)h(Bruen)f(and)g (R.)g(Dixon)h([1975],)d(The)i Fe(n)p Fj(-queen)g(problem,)g Fi(Discr)l(ete)i(Math.)704 3321 y Fc(12)p Fj(,)27 b(393{395.)515 3429 y(121.)40 b(P)-7 b(.)35 b(Buneman)g(and)g(L.)g(Levy)g([1980],)e (The)j(to)n(w)n(ers)d(of)i(Hanoi)g(problem,)g Fi(Inform.)704 3528 y(Pr)l(o)l(c)l(ess.)30 b(L)l(ett.)e Fc(10)p Fj(,)f(243{244.)515 3636 y(122.)40 b(A.)23 b(P)-7 b(.)23 b(Burger,)f(E.)h(J.)g(Co)r(c)n(k) -5 b(a)n(yne)22 b(and)h(C.)g(M.)h(Mynhardt)f([1977],)e(Domination)i (and)704 3736 y(irredundance)j(in)i(the)g(queen's)g(graph,)e Fi(Discr)l(ete)k(Math.)f Fc(163)p Fj(,)e(47{66.)515 3844 y(123.)40 b(D.)23 b(W.)f(Busha)n(w)g([1967],)e(On)i(the)h(name)f(and)g (history)g(of)g(Nim,)h Fi(Washington)j(Math.)704 3944 y Fc(11)p Fj(,)h(Oct.)h(1966.)d(Reprin)n(ted)j(in:)g Fi(NY)h(State)g(Math.)i(T)-6 b(e)l(achers)31 b(J.)p Fj(,)d Fc(17)p Fj(,)f(pp.)h(52{55.)515 4051 y(124.)40 b(J.-Y.)35 b(Cai,)h(A.)g(Condon)f(and)h(R.)g(J.)g(Lipton)g([1992],)e(On)h(games)g (of)h(incomplete)704 4151 y(information,)27 b Fi(The)l(or)l(et.)k (Comput.)f(Sci.)f Fc(103)p Fj(,)e(25{38.)515 4259 y(125.)40 b(I.)32 b(Caines,)g(C.)g(Gates,)g(R.)g(K.)g(Guy)g(and)g(R.)h(J.)f(No)n (w)n(ak)n(o)n(wski)d([1999],)h(P)n(erio)r(ds)h(in)704 4359 y(taking)c(and)g(splitting)h(games,)f Fi(A)n(mer.)j(Math.)h (Monthly)36 b Fc(106)p Fj(,)27 b(359{361.)515 4467 y(126.)40 b(D.)29 b(Calistrate)e([1996],)f(The)i(reduced)g(canonical)f(form)h(of) g(a)f(game,)h(in:)g Fi(Games)j(of)704 4566 y(No)h(Chanc)l(e,)i Fj(Pro)r(c.)29 b(MSRI)i(W)-7 b(orkshop)29 b(on)h(Com)n(binatorial)f (Games,)h(July)-7 b(,)30 b(1994,)704 4666 y(Berk)n(eley)-7 b(,)33 b(CA,)h(MSRI)h(Publ.)f(\(R.)h(J.)f(No)n(w)n(ak)n(o)n(wski,)e (ed.\),)j(V)-7 b(ol.)34 b(29,)f(Cam)n(bridge)704 4765 y(Univ)n(ersit)n(y)27 b(Press,)f(Cam)n(bridge,)g(pp.)i(409{416.)515 4873 y(127.)40 b(C.)34 b(Cannings)e(and)i(J.)f(Haigh)h([1992],)e(Mon)n (treal)g(solitaire,)g Fi(J.)k(Combin.)g(The)l(ory)704 4973 y Fj(\(Ser.)27 b(A\))i Fc(60)p Fj(,)e(50{66.)p eop %%Page: 14 14 14 13 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(14)515 523 y(128.)40 b(A.)28 b(K.)f(Chandra,)g(D.)h(C.)g(Kozen)f(and)g(L.)h(J.)f(Sto)r(c)n(kmey)n (er)g([1981],)f(Alternation,)h Fi(J.)704 623 y(Asso)l(c.)j(Comput.)g (Mach.)g Fc(28)p Fj(,)d(114{133.)515 731 y(129.)40 b(A.)27 b(K.)f(Chandra)g(and)g(L.)h(J.)f(Sto)r(c)n(kmey)n(er)g([1976],)f (Alternation,)h Fi(Pr)l(o)l(c.)k(17th)g(A)n(nn.)704 830 y(Symp.)d(F)-6 b(oundations)27 b(of)h(Computer)f(Scienc)l(e)33 b Fj(\(Houston,)24 b(TX,)h(Oct.)f(1976\),)f(IEEE)704 930 y(Computer)k(So)r(c.,)h(Long)e(Beac)n(h,)h(CA,)h(pp.)g(98{108.)515 1038 y(130.)40 b(S.)23 b(M.)f(Chase)g([1972],)f(An)h(implemen)n(ted)i (graph)d(algorithm)g(for)h(winning)g(Shannon)704 1137 y(switc)n(hing)27 b(games,)g Fi(Commun.)j(Asso)l(c.)g(Comput.)g(Mach.)g Fc(15)p Fj(,)d(253{256.)515 1245 y(131.)40 b(B.)c(S.)g(Chlebus)g ([1986],)e(Domino-tiling)i(games,)e Fi(J.)k(Comput.)g(System)f(Sci.)f Fc(32)p Fj(,)704 1345 y(374{392.)515 1453 y(132.)k(F.)32 b(R.)g(K.)f(Ch)n(ung)g([1989],)f(P)n(ebbling)h(in)g(h)n(yp)r(ercub)r (es,)h Fi(SIAM)h(J.)g(Disc.)h(Math.)f Fc(2)p Fj(,)704 1553 y(467{472.)515 1660 y(133.)40 b(F.)34 b(R.)g(K.)g(Ch)n(ung,)f(J.)h (E.)f(Cohen)h(and)g(R.)g(L.)g(Graham)f([1988],)f(Pursuit-ev)-5 b(asion)704 1760 y(games)26 b(on)i(graphs,)e Fi(J.)k(Gr)l(aph)h(The)l (ory)36 b Fc(12)p Fj(,)27 b(159{167.)515 1868 y(134.)40 b(F.)f(Ch)n(ung,)g(R.)h(Graham,)e(J.)h(Morrison)e(and)i(A.)h(Odlyzk)n (o)e([1995],)f(P)n(ebbling)h(a)704 1968 y(c)n(hessb)r(oard,)26 b Fi(A)n(mer.)k(Math.)h(Monthly)36 b Fc(102)p Fj(,)27 b(113{123.)515 2076 y(135.)40 b(V.)33 b(Ch)n(v\023)-42 b(atal)32 b([1973],)f(On)i(the)g(computational)f(complexit)n(y)h(of)f (\014nding)h(a)g(k)n(ernel,)704 2175 y(Rep)r(ort)i(No.)h(CRM-300,)e (Cen)n(tre)h(de)h(Rec)n(herc)n(hes)e(Math)n(\023)-39 b(ematiques,)35 b(Univ)n(ersit)n(\023)-39 b(e)704 2275 y(de)28 b(Mon)n(tr)n(\023)-39 b(eal.)515 2383 y(136.)40 b(V.)22 b(Ch)n(v\023)-42 b(atal)21 b([1981],)f(Cheap,)i(middling)g(or)f (dear,)g(in:)h Fi(The)k(Mathematic)l(al)g(Gar)l(dner)704 2482 y Fj(\(D.)i(A.)g(Klarner,)e(ed.\),)i(W)-7 b(adsw)n(orth)27 b(In)n(ternat.,)g(Belmon)n(t,)g(CA,)h(pp.)g(44{50.)515 2590 y(137.)40 b(V.)28 b(Ch)n(v\023)-42 b(atal)26 b([1983],)g (Mastermind,)i Fi(Combinatoric)l(a)36 b Fc(3)p Fj(,)28 b(325{329.)515 2698 y(138.)40 b(V.)34 b(Ch)n(v\023)-42 b(atal)33 b(and)h(P)-7 b(.)34 b(Erd})-42 b(os)32 b([1978],)g(Biased)i (p)r(ositional)f(games,)g Fi(A)n(nn.)i(Discr)l(ete)704 2798 y(Math.)29 b Fc(2)p Fj(,)f(221{229,)d(Algorithmic)j(Asp)r(ects)h (of)f(Com)n(binatorics,)e(\(B.)j(Alspac)n(h,)e(P)-7 b(.)704 2897 y(Hell)32 b(and)f(D.)h(J.)f(Miller,)h(eds.\),)f(Qualicum)h(Beac)n (h,)e(BC,)i(Canada,)e(1976,)g(North-)704 2997 y(Holland.)515 3105 y(139.)40 b(F.)28 b(Cicalese)g(and)g(U.)g(V)-7 b(accaro)27 b([2000],)f(Optimal)i(strategies)f(against)g(a)h(liar,)f Fi(The-)704 3205 y(or)l(et.)j(Comput.)g(Sci.)h Fj(\(Math)d(Games\))f Fc(230)p Fj(,)g(167{193.)515 3313 y(140.)40 b(C.)i(Clark)e([1996],)g (On)i(ac)n(hieving)e(c)n(hannels)h(in)h(a)f(bip)r(olar)g(game,)g(in:)h Fi(Afric)l(an)704 3412 y(A)n(meric)l(ans)24 b(in)h(Mathematics)33 b Fj(\(Piscata)n(w)n(a)n(y)-7 b(,)19 b(NJ,)j(1996\),)e(DIMA)n(CS)j (Ser.)e(Discrete)704 3512 y(Math.)28 b(Theoret.)e(Comput.)i(Sci.,)g(V) -7 b(ol.)28 b(34,)e(Amer.)i(Math.)g(So)r(c.,)f(Pro)n(vidence,)f(RI,)704 3611 y(pp.)i(23{27.)515 3719 y(141.)40 b(D.)d(S.)h(Clark)e([1986],)f (Fib)r(onacci)i(n)n(um)n(b)r(ers)f(as)h(exp)r(ected)g(v)-5 b(alues)37 b(in)g(a)g(game)f(of)704 3819 y(c)n(hance,)27 b Fi(Fib)l(onac)l(ci)k(Quart.)d Fc(24)p Fj(,)f(263{267.)515 3927 y(142.)40 b(E.)32 b(J.)h(Co)r(c)n(k)-5 b(a)n(yne)31 b([1990],)g(Chessb)r(oard)g(domination)h(problems,)g Fi(Discr)l(ete)j(Math.)704 4027 y Fc(86)p Fj(,)27 b(13{20.)515 4134 y(143.)40 b(E.)24 b(J.)g(Co)r(c)n(k)-5 b(a)n(yne)23 b(and)i(S.)f(T.)h(Hedetniemi)g([1986],)e(On)h(the)h(diagonal)e(queens)i (dom-)704 4234 y(ination)i(problem,)g Fi(J.)j(Combin.)h(The)l(ory)39 b Fj(\(Ser.)27 b(A\))i Fc(42)p Fj(,)e(137{139.)515 4342 y(144.)40 b(A.)f(J.)f(Cole)g(and)g(A.)h(J.)f(T.)h(Da)n(vie)f([1969],)e (A)j(game)f(based)g(on)g(the)h(Euclidean)704 4442 y(algorithm)26 b(and)i(a)f(winning)h(strategy)e(for)h(it,)h Fi(Math.)j(Gaz.)e Fc(53)p Fj(,)e(354{357.)515 4550 y(145.)40 b(D.)28 b(B.)g(Coleman)e ([1978],)g(Stretc)n(h:)i(a)f(geob)r(oard)f(game,)h Fi(Math.)k(Mag.)e Fc(51)p Fj(,)e(49{54.)515 4658 y(146.)40 b(A.)32 b(Condon)f([1989],)f Fi(Computational)35 b(Mo)l(dels)f(of)h(Games)7 b Fj(,)32 b(A)n(CM)g(Distinguished)704 4757 y(Dissertation,)27 b(MIT)g(Press,)g(Cam)n(bridge,)f(MA.)515 4865 y(147.)40 b(A.)27 b(Condon)g([1991],)e(Space-b)r(ounded)i(probabilistic)g(game)f (automata,)g Fi(J.)k(Asso)l(c.)704 4965 y(Comput.)g(Mach.)g Fc(38)p Fj(,)d(472{494.)p eop %%Page: 15 15 15 14 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(15)515 523 y(148.)40 b(A.)32 b(Condon)f([1992],)g(The)g(complexit)n(y)h(of)g(Sto)r(c)n(hastic)f (games,)g Fi(Information)j(and)704 623 y(Computation)h Fc(96)p Fj(,)27 b(203{224.)515 731 y(149.)40 b(A.)22 b(Condon)g([1993],)e(On)i(algorithms)f(for)h(simple)g(sto)r(c)n(hastic) f(games,)g(in:)i Fi(A)l(dvanc)l(es)704 830 y(in)28 b(c)l(omputational)g (c)l(omplexity)h(the)l(ory)35 b Fj(\(New)26 b(Brunswic)n(k,)e(NJ,)i (1990\),)d(DIMA)n(CS)704 930 y(Ser.)37 b(Discrete)h(Math.)g(Theoret.)f (Comput.)h(Sci.,)g(V)-7 b(ol.)38 b(13,)e(Amer.)i(Math.)g(So)r(c.,)704 1029 y(Pro)n(vidence,)26 b(RI,)h(pp.)h(51{71.)515 1137 y(150.)40 b(A.)29 b(Condon,)g(J.)g(F)-7 b(eigen)n(baum,)29 b(C.)g(Lund)h(and)f(P)-7 b(.)29 b(Shor)g([1993],)e(Probabilistically) 704 1237 y(c)n(hec)n(k)-5 b(able)20 b(debate)i(systems)f(and)g(appro)n (ximation)e(algorithms)i(for)f(PSP)-7 b(A)n(CE-hard)704 1337 y(functions,)19 b Fi(Pr)l(o)l(c.)k(25th)f(A)n(nn.)g(A)n(CM)g (Symp.)g(The)l(ory)i(of)e(Computing,)h Fj(Asso)r(c.)c(Com-)704 1436 y(put.)28 b(Mac)n(h.,)f(New)h(Y)-7 b(ork,)27 b(NY)r(,)h(pp.)g (305{314.)515 1544 y(151.)40 b(A.)21 b(Condon)g(and)g(R.)g(E.)g(Ladner) f([1988],)g(Probabilistic)f(game)i(automata,)f Fi(J.)k(Com-)704 1644 y(put.)36 b(System)f(Sci.)g Fc(36)p Fj(,)e(452{489,)e(preliminary) i(v)n(ersion)g(in:)h(Pro)r(c.)f(Structure)h(in)704 1743 y(complexit)n(y)f(theory)g(\(Berk)n(eley)-7 b(,)32 b(CA,)i(1986\),)e (Lecture)i(Notes)f(in)h(Comput.)g(Sci.,)704 1843 y(V)-7 b(ol.)27 b(223,)g(Springer,)f(Berlin,)i(pp.)g(144{162.)515 1951 y(152.)40 b(I.)34 b(G.)h(Connell)f([1959],)f(A)i(generalization)d (of)j(Wytho\013)6 b('s)35 b(game,)f Fi(Canad.)k(Math.)704 2051 y(Bul)t(l.)29 b Fc(2)p Fj(,)e(181{190.)515 2159 y(153.)40 b(J.)34 b(H.)h(Con)n(w)n(a)n(y)d([1972],)h(All)i(n)n(um)n(b)r (ers)f(great)f(and)h(small,)h(Res.)f(P)n(ap)r(er)f(No.)h(149,)704 2258 y(Univ.)28 b(of)f(Calgary)f(Math.)i(Dept.)515 2366 y(154.)40 b(J.)j(H.)g(Con)n(w)n(a)n(y)f([1976],)f Fi(On)i(Numb)l(ers)h (and)g(Games)7 b Fj(,)44 b(Academic)f(Press,)f(Lon-)704 2466 y(don,)25 b(translated)f(in)n(to)h(German:)1796 2445 y Fi(\177)1781 2466 y(Ub)l(er)i(Zahlen)h(und)f(Spiele)f Fj(b)n(y)f(Brigitte)g(Kunisc)n(h,)704 2565 y(F)-7 b(riedr.)27 b(View)n(eg)g(&)g(Sohn,)h(Braunsc)n(h)n(w)n(eig,)d(1983.)515 2673 y(155.)40 b(J.)21 b(H.)h(Con)n(w)n(a)n(y)d([1977],)h(All)h(games)g (brigh)n(t)f(and)h(b)r(eautiful,)i Fi(A)n(mer.)h(Math.)h(Monthly)704 2773 y Fc(84)p Fj(,)i(417{434.)515 2881 y(156.)40 b(J.)27 b(H.)h(Con)n(w)n(a)n(y)e([1978],)g(A)i(gam)n(ut)f(of)g(game)g (theories,)g Fi(Math.)k(Mag.)e Fc(51)p Fj(,)e(5{12.)515 2989 y(157.)40 b(J.)29 b(H.)h(Con)n(w)n(a)n(y)e([1978],)g(Lo)r(op)n(y)g (Games,)h Fi(A)n(nn.)i(Discr)l(ete)h(Math.)f Fc(3)p Fj(,)e(55{74,)e (Pro)r(c.)704 3088 y(Symp.)38 b(Adv)-5 b(ances)38 b(in)g(Graph)f (Theory)-7 b(,)37 b(Cam)n(bridge)g(Com)n(binatorial)f(Conf.)i(\(B.)704 3188 y(Bollob\023)-42 b(as,)26 b(ed.\),)i(Cam)n(bridge,)e(Ma)n(y)h (1977.)515 3296 y(158.)40 b(J.)23 b(H.)h(Con)n(w)n(a)n(y)d([1990],)h (In)n(tegral)g(lexicographic)f(co)r(des,)i Fi(Discr)l(ete)j(Math.)f Fc(83)p Fj(,)e(219{)704 3396 y(235.)515 3504 y(159.)40 b(J.)35 b(H.)g(Con)n(w)n(a)n(y)e([1991],)g(More)h(w)n(a)n(ys)g(of)h (com)n(bining)f(games,)g(in:)h Fi(Combinatorial)704 3603 y(Games,)c Fj(Pro)r(c.)26 b(Symp.)i(Appl.)g(Math.)g(\(R.)g(K.)f(Guy)-7 b(,)28 b(ed.\),)g(V)-7 b(ol.)28 b(43,)e(Amer.)i(Math.)704 3703 y(So)r(c.,)f(Pro)n(vidence,)f(RI,)i(pp.)g(57{71.)515 3811 y(160.)40 b(J.)22 b(H.)g(Con)n(w)n(a)n(y)e([1991],)g(Num)n(b)r (ers)i(and)f(games,)g(in:)i Fi(Combinatorial)k(Games,)e Fj(Pro)r(c.)704 3910 y(Symp.)34 b(Appl.)g(Math.)g(\(R.)g(K.)f(Guy)-7 b(,)33 b(ed.\),)h(V)-7 b(ol.)34 b(43,)f(Amer.)g(Math.)h(So)r(c.,)f(Pro) n(vi-)704 4010 y(dence,)28 b(RI,)f(pp.)h(23{34.)515 4118 y(161.)40 b(J.)29 b(H.)h(Con)n(w)n(a)n(y)d([1996],)h(The)h(angel)f (problem,)h(in:)h Fi(Games)i(of)g(No)f(Chanc)l(e,)i Fj(Pro)r(c.)704 4218 y(MSRI)20 b(W)-7 b(orkshop)18 b(on)i(Com)n(binatorial)e(Games,)h (July)-7 b(,)19 b(1994,)f(Berk)n(eley)-7 b(,)19 b(CA,)h(MSRI)704 4317 y(Publ.)k(\(R.)h(J.)f(No)n(w)n(ak)n(o)n(wski,)e(ed.\),)i(V)-7 b(ol.)25 b(29,)e(Cam)n(bridge)g(Univ)n(ersit)n(y)h(Press,)f(Cam-)704 4417 y(bridge,)k(pp.)h(3{12.)515 4525 y(162.)40 b(J.)e(H.)g(Con)n(w)n (a)n(y)e(and)h(H.)i(S.)f(M.)g(Co)n(xeter)f([1973],)f(T)-7 b(riangulated)37 b(p)r(olygons)f(and)704 4624 y(frieze)27 b(patterns,)g Fi(Math.)k(Gaz.)e Fc(57)p Fj(,)e(87{94;)f(175{183.)515 4732 y(163.)40 b(J.)30 b(H.)h(Con)n(w)n(a)n(y)d(and)i(N.)h(J.)f(A.)h (Sloane)e([1986],)g(Lexicographic)f(co)r(des:)i(error-cor-)704 4832 y(recting)22 b(co)r(des)g(from)g(game)g(theory)-7 b(,)22 b Fi(IEEE)k(T)-6 b(r)l(ans.)26 b(Inform.)g(The)l(ory)31 b Fc(IT-32)p Fj(,)23 b(337{)704 4932 y(348.)p eop %%Page: 16 16 16 15 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(16)515 523 y(164.)40 b(M.)e(L.)g(Co)r (ok)f(and)h(L.)g(E.)f(Shader)h([1979],)e(A)i(strategy)f(for)g(the)i (Ramsey)e(game)704 623 y(\\Tritip",)c Fi(Pr)l(o)l(c.)k(10th)f(Southe)l (ast.)g(Conf.)h(Combinatorics,)h(Gr)l(aph)f(The)l(ory)g(and)704 722 y(Computing,)32 b(Bo)l(c)l(a)g(R)l(aton)6 b Fj(,)28 b(V)-7 b(ol.)29 b(1)g(of)g Fi(Congr.)j(Numer.)e(23,)i Fj(Utilitas)e(Math.,)f(pp.)704 822 y(315{324.)515 930 y(165.)40 b(M.)34 b(Copp)r(er)g([1993],)f(Graph)h(theory)f(and)i(the)f (game)g(of)g(sprouts,)g Fi(A)n(mer.)i(Math.)704 1029 y(Monthly)g Fc(100)p Fj(,)27 b(478{482.)515 1137 y(166.)40 b(M.)34 b(Cornelius)f(and)h(A.)h(P)n(arr)d([1991],)g Fi(What's)37 b(Y)-6 b(our)35 b(Game?)10 b Fj(,)35 b(Cam)n(bridge)e (Uni-)704 1237 y(v)n(ersit)n(y)26 b(Press,)g(Cam)n(bridge.)515 1345 y(167.)40 b(H.)d(S.)f(M.)h(Co)n(xeter)e([1953],)g(The)i(golden)e (section,)i(ph)n(yllotaxis)e(and)h(Wytho\013)6 b('s)704 1445 y(game,)27 b Fi(Scripta)j(Math.)f Fc(19)p Fj(,)e(135{143.)515 1553 y(168.)40 b(J.)29 b(W.)i(Creely)e([1987],)f(The)i(length)f(of)h(a) g(t)n(w)n(o-n)n(um)n(b)r(er)e(game,)h Fi(Fib)l(onac)l(ci)k(Quart.)704 1652 y Fc(25)p Fj(,)27 b(174{179.)515 1760 y(169.)40 b(J.)24 b(W.)h(Creely)f([1988],)f(The)i(length)g(of)g(a)f(three-n)n(um) n(b)r(er)g(game,)g Fi(Fib)l(onac)l(ci)k(Quart.)704 1860 y Fc(26)p Fj(,)f(141{143.)515 1968 y(170.)40 b(H.)24 b(T.)g(Croft)f([1964],)g(`Lion)g(and)h(man':)g(a)f(p)r(ostscript,)h Fi(J.)i(L)l(ondon)g(Math.)i(So)l(c.)c Fc(39)p Fj(,)704 2067 y(385{390.)515 2175 y(171.)40 b(D.)h(W.)g(Cro)n(w)n(e)e([1956],)g (The)i Fe(n)p Fj(-dimensional)f(cub)r(e)h(and)f(the)h(to)n(w)n(er)f(of) g(Hanoi,)704 2275 y Fi(A)n(mer.)30 b(Math.)h(Monthly)36 b Fc(63)p Fj(,)27 b(29{30.)515 2383 y(172.)40 b(L.)34 b(Csirmaz)f([1980],)f(On)h(a)h(com)n(binatorial)e(game)h(with)h(an)g (application)f(to)h(Go-)704 2482 y(Moku,)27 b Fi(Discr)l(ete)j(Math.)f Fc(29)p Fj(,)e(19{23.)515 2590 y(173.)40 b(L.)25 b(Csirmaz)f(and)h(Z.)h (Nagy)e([1979],)g(On)h(a)f(generalization)g(of)h(the)h(game)e(Go-Moku) 704 2690 y(I)r(I,)k Fi(Studia)i(Sci.)g(Math.)h(Hung.)c Fc(14)p Fj(,)h(461{469.)515 2798 y(174.)40 b(J.)c(Culb)r(erson)h ([1999],)e(Sok)n(oban)g(is)i(PSP)-7 b(A)n(CE)35 b(complete,)i(in:)g Fi(F)-6 b(un)37 b(With)i(A)n(lgo-)704 2897 y(rithms)7 b Fj(,)21 b(V)-7 b(ol.)21 b(4)g(of)g Fi(Pr)l(o)l(c)l(e)l(e)l(dings)j (in)g(Informatics)7 b Fj(,)22 b(Carleton)e(Scien)n(ti\014c,)h(Univ)n (ersit)n(y)704 2997 y(of)27 b(W)-7 b(aterlo)r(o,)27 b(W)-7 b(aterlo)r(o,)27 b(On)n(t.,)g(pp.)h(65{76.)515 3105 y(175.)40 b(P)-7 b(.)29 b(Cull)h(and)f(E.)g(F.)h(Ec)n(klund,)f(Jr.)f([1982],)g (On)h(the)h(to)n(w)n(ers)e(of)h(Hanoi)g(and)g(gener-)704 3205 y(alized)e(to)n(w)n(ers)f(of)i(Hanoi)f(problems,)g Fi(Congr.)k(Numer.)c Fc(35)p Fj(,)g(229{238.)515 3313 y(176.)40 b(P)-7 b(.)37 b(Cull)h(and)f(E.)g(F.)h(Ec)n(klund,)f(Jr.)g ([1985],)f(T)-7 b(o)n(w)n(ers)35 b(of)j(Hanoi)f(and)g(analysis)f(of)704 3412 y(algorithms,)26 b Fi(A)n(mer.)k(Math.)h(Monthly)36 b Fc(92)p Fj(,)27 b(407{420.)515 3520 y(177.)40 b(P)-7 b(.)27 b(Cull)i(and)e(C.)h(Geret)n(y)f([1985],)g(Is)g(to)n(w)n(ers)f (of)i(Hanoi)g(really)e(hard?,)i Fi(Congr.)j(Nu-)704 3620 y(mer.)d Fc(47)p Fj(,)f(237{242.)515 3728 y(178.)40 b(J.)28 b(Czyzo)n(wicz,)e(D.)j(Mundici)g(and)f(A.)g(P)n(elc)f([1988],)g (Solution)h(of)g(Ulam's)g(problem)704 3827 y(on)f(binary)g(searc)n(h)f (with)i(t)n(w)n(o)f(lies,)g Fi(J.)j(Combin.)h(The)l(ory)39 b Fj(\(Ser.)28 b(A\))g Fc(49)p Fj(,)f(384{388.)515 3935 y(179.)40 b(J.)26 b(Czyzo)n(wicz,)e(D.)j(Mundici)f(and)g(A.)g(P)n(elc)f ([1989],)g(Ulam's)g(searc)n(hing)f(game)i(with)704 4035 y(lies,)h Fi(J.)j(Combin.)h(The)l(ory)39 b Fj(\(Ser.)27 b(A\))i Fc(52)p Fj(,)e(62{76.)515 4143 y(180.)40 b(G.)27 b(Danara)5 b(j)26 b(and)h(V.)h(Klee)f([1977],)e(The)i(connectedness)g (game)f(and)h(the)h Fe(c)p Fj(-comp-)704 4242 y(lexit)n(y)f(of)h (certain)f(graphs,)f Fi(SIAM)j(J.)h(Appl.)h(Math.)e Fc(32)p Fj(,)e(431{442.)515 4350 y(181.)40 b(C.)20 b(Darb)n(y)f(and)h(R.)h(La)n (v)n(er)d([1998],)g(Coun)n(table)i(length)g(Ramsey)f(games,)h Fi(Set)i(the)l(ory:)704 4450 y(te)l(chniques)f(and)h(applic)l(ations.)i Fj(Pro)r(c.)17 b(of)i(the)f(conferences,)g(Curacao,)e(Netherlands)704 4550 y(An)n(tilles,)27 b(June)g(26{30,)d(1995)h(and)i(Barcelona,)d (Spain,)j(June)g(10{14,)e(1996)f(\(C.)k(A.)704 4649 y(Di)g(Prisco)e(et) i(al.,)f(eds.\),)h(Klu)n(w)n(er,)e(Dordrec)n(h)n(t,)h(pp.)h(41{46.)515 4757 y(182.)40 b(A.)28 b(L.)f(Da)n(vies)g([1970],)f(Rotating)h(the)h (\014fteen)h(puzzle,)e Fi(Math.)k(Gaz.)e Fc(54)p Fj(,)e(237{240.)515 4865 y(183.)40 b(M.)20 b(Da)n(vis)e([1963],)g(In\014nite)j(games)d(of)h (p)r(erfect)h(information,)f Fi(A)n(nn.)j(of)h(Math.)h(Stud.,)704 4965 y(Princ)l(eton)34 b Fc(52)p Fj(,)27 b(85{101.)p eop %%Page: 17 17 17 16 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(17)515 523 y(184.)40 b(R.)22 b(W.)h(Da)n(w)n(es)f([1992],)e(Some)j(pursuit-ev)-5 b(asion)21 b(problems)g(on)h(grids,)g Fi(Inform.)k(Pr)l(o-)704 623 y(c)l(ess.)k(L)l(ett.)d Fc(43)p Fj(,)h(241{247.)515 731 y(185.)40 b(T.)28 b(R.)f(Da)n(wson)g([1934],)f(Problem)g(1603,)g Fi(F)-6 b(airy)31 b(Chess)g(R)l(eview)37 b Fj(p.)28 b(94,)e(Dec.)515 839 y(186.)40 b(T.)32 b(R.)h(Da)n(wson)f([1935],)f(Caissa's)g(Wild)i (Roses,)e(reprin)n(ted)h(in:)h Fi(Five)i(Classics)h(of)704 938 y(F)-6 b(airy)31 b(Chess)p Fj(,)d(Do)n(v)n(er,)f(1973.)515 1046 y(187.)40 b(N.)32 b(G.)f(de)h(Bruijn)f([1972],)f(A)h(solitaire)f (game)h(and)g(its)g(relation)g(to)g(a)g(\014nite)h(\014eld,)704 1146 y Fi(J.)e(R)l(e)l(cr.)f(Math.)g Fc(5)p Fj(,)f(133{137.)515 1254 y(188.)40 b(N.)24 b(G.)h(de)f(Bruijn)h([1981],)d(Pretzel)h (Solitaire)h(as)f(a)h(pastime)g(for)g(the)h(lonely)e(mathe-)704 1353 y(matician,)i(in:)h Fi(The)j(Mathematic)l(al)i(Gar)l(dner)k Fj(\(D.)27 b(A.)f(Klarner,)e(ed.\),)i(W)-7 b(adsw)n(orth)704 1453 y(In)n(ternat.,)27 b(Belmon)n(t,)g(CA,)h(pp.)g(16{24.)515 1561 y(189.)40 b(F.)32 b(de)f(Carteblanc)n(he)f([1970],)g(The)i (princess)e(and)i(the)g(roses,)e Fi(J.)j(R)l(e)l(cr.)g(Math.)g Fc(3)p Fj(,)704 1660 y(238{239.)515 1768 y(190.)40 b(F.)33 b(deCarte)g(Blanc)n(he)f([1974],)g(The)h(roses)f(and)h(the)g(princes,)g Fi(J.)i(R)l(e)l(cr.)g(Math.)f Fc(7)p Fj(,)704 1868 y(295{298.)515 1976 y(191.)40 b(A.)28 b(P)-7 b(.)27 b(DeLoac)n(h)g([1971],)f(Some)h (in)n(v)n(estigations)f(in)n(to)i(the)g(game)f(of)g(SIM,)h Fi(J.)i(R)l(e)l(cr.)704 2076 y(Math.)f Fc(4)p Fj(,)e(36{41.)515 2183 y(192.)40 b(H.)25 b(de)g(P)n(arville)d([1884],)h(La)h(tour)g (d'Hano)-9 b(\177)-32 b(\020)24 b(et)h(la)f(question)g(du)h(T)-7 b(onkin,)25 b Fi(L)l(a)i(Natur)l(e)704 2283 y Fc(12)p Fj(,)g(285{286.)515 2391 y(193.)40 b(B.)26 b(Descartes)g([1953],)e(Wh)n (y)j(are)e(series)g(m)n(usical?,)h Fi(Eur)l(eka)34 b Fc(16)p Fj(,)26 b(18{20,)e(reprin)n(ted)704 2491 y Fi(ibid.)30 b Fc(27)d Fj(\(1964\))f(29{31.)515 2599 y(194.)40 b(A.)35 b(K.)g(Dewdney)g([1984)e({)h(],)h(Computer)g(Recreations,)e(a)i(column) g(in)g(Scien)n(ti\014c)704 2698 y(American)27 b(\(since)h(Ma)n(y)-7 b(,)27 b(1984\).)515 2806 y(195.)40 b(C.)33 b(G.)g(Dideric)n(h)f ([1995],)g(Bibliograph)n(y)e(on)j(minimax)g(game)f(theory)-7 b(,)32 b(sequen)n(tial)704 2906 y(and)27 b(parallel)g(algorithms.)704 3005 y(h)n(ttp://diwww.ep\015.c)n(h/)p Ff(\030)p Fj(dideric)n (h/bibliographies.h)n(tml)515 3113 y(196.)40 b(R.)23 b(Diestel)g(and)f(I.)h(Leader)f([1994],)f(Domination)h(games)g(on)g (in\014nite)i(graphs,)d Fi(The-)704 3213 y(or)l(et.)30 b(Comput.)g(Sci.)h Fj(\(Math)d(Games\))f Fc(132)p Fj(,)g(337{345.)515 3321 y(197.)40 b(T.)28 b(Dinski)h(and)g(X.)f(Zh)n(u)h([1999],)d(A)j(b)r (ound)g(for)f(the)h(game)f(c)n(hromatic)f(n)n(um)n(b)r(er)h(of)704 3421 y(graphs,)e Fi(Discr)l(ete)k(Math.)f Fc(196)p Fj(,)e(109{115.)515 3528 y(198.)40 b(A.)g(P)-7 b(.)39 b(Domory)n(ad)f([1964],)g Fi(Mathematic)l(al)43 b(Games)f(and)f(Pastimes)7 b Fj(,)41 b(P)n(ergamon)704 3628 y(Press,)26 b(Oxford,)h(translated)f(b)n(y)i(H.) g(Moss.)515 3736 y(199.)40 b(A.)c(Dress,)f(A.)h(Flammenk)-5 b(amp)36 b(and)f(N.)h(Pink)g([1999],)e(Additiv)n(e)i(p)r(erio)r(dicit)n (y)f(of)704 3836 y(the)30 b(Sprague-Grundy)f(function)h(of)h(certain)e (Nim)i(games,)e Fi(A)l(dv.)j(in)g(Appl.)i(Math.)704 3935 y Fc(22)p Fj(,)27 b(249{270.)515 4043 y(200.)40 b(P)-7 b(.)25 b(Duc)n(het)i([1980],)d(Graphes)h(no)n(y)n(au-parfaits,)e Fi(A)n(nn.)28 b(Discr)l(ete)g(Math.)f Fc(9)p Fj(,)f(93{101.)515 4151 y(201.)40 b(P)-7 b(.)26 b(Duc)n(het)h([1987],)e(A)i(su\016cien)n (t)g(condition)f(for)h(a)f(digraph)f(to)i(b)r(e)g(k)n(ernel-p)r (erfect,)704 4251 y Fi(J.)j(Gr)l(aph)h(The)l(ory)36 b Fc(11)p Fj(,)27 b(81{85.)515 4359 y(202.)40 b(P)-7 b(.)27 b(Duc)n(het)g([1987],)e(P)n(arit)n(y)g(graphs)h(are)g(k)n(ernel-M-solv) -5 b(able,)25 b Fi(J.)k(Combin.)h(The)l(ory)704 4458 y Fj(\(Ser.)d(B\))h Fc(43)p Fj(,)f(121{126.)515 4566 y(203.)40 b(P)-7 b(.)22 b(Duc)n(het)g(and)g(H.)h(Meyniel)f([1981],)e(A) i(note)g(on)g(k)n(ernel-critical)e(graphs,)h Fi(Discr)l(ete)704 4666 y(Math.)29 b Fc(33)p Fj(,)e(103{105.)515 4774 y(204.)40 b(P)-7 b(.)30 b(Duc)n(het)i(and)e(H.)h(Meyniel)g([1983],)e(Une)i(g)n (\023)-39 b(en)n(\023)g(eralisation)27 b(du)k(th)n(\023)-39 b(eor)n(\022)g(eme)28 b(de)j(Ri-)704 4873 y(c)n(hardson)19 b(sur)i(l'existence)g(de)g(no)n(y)n(aux)f(dans)h(le)g(graphes)f(orien)n (t)n(\023)-39 b(es,)19 b Fi(Discr)l(ete)24 b(Math.)704 4973 y Fc(43)p Fj(,)j(21{27.)p eop %%Page: 18 18 18 17 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(18)515 523 y(205.)40 b(P)-7 b(.)39 b(Duc)n(het)g(and)g(H.)h(Meyniel)f([1993],)f(Kernels)g(in)h (directed)g(graphs:)f(a)h(p)r(oison)704 623 y(game,)27 b Fi(Discr)l(ete)i(Math.)g Fc(115)p Fj(,)e(273{276.)515 731 y(206.)40 b(H.)28 b(E.)f(Dudeney)h([1958],)e Fi(The)31 b(Canterbury)f(Puzzles)7 b Fj(,)28 b(Mineola,)f(NY,)h(4th)f(edn.)515 839 y(207.)40 b(H.)31 b(E.)f(Dudeney)h([1989],)e Fi(A)n(musements)i(in) i(Mathematics)7 b Fj(,)32 b(reprin)n(ted)e(b)n(y)g(Do)n(v)n(er,)704 938 y(Mineola,)d(NY.)515 1046 y(208.)40 b(N.)35 b(Duvdev)-5 b(ani)36 b(and)f(A.)h(S.)f(F)-7 b(raenk)n(el)34 b([1989],)f(Prop)r (erties)h(of)h Fe(k)s Fj(-W)-7 b(elter's)35 b(game,)704 1146 y Fi(Discr)l(ete)30 b(Math.)f Fc(76)p Fj(,)e(197{221.)515 1254 y(209.)40 b(J.)26 b(Edmonds)f([1965],)g(Lehman's)g(switc)n(hing)h (game)f(and)h(a)g(theorem)f(of)h(T)-7 b(utte)27 b(and)704 1353 y(Nash{Williams,)g Fi(J.)j(R)l(es.)f(Nat.)h(Bur.)g(Standar)l(ds)35 b Fc(69B)p Fj(,)27 b(73{77.)515 1461 y(210.)40 b(R.)c(Ehren)n(b)r(org)e (and)i(E.)f(Steingr)-9 b(\023)-32 b(\020msson)34 b([1996],)g(Pla)n (ying)h(Nim)h(on)g(a)f(simplicial)704 1561 y(complex,)27 b Fi(Ele)l(ctr)l(onic)k(J.)e(Combin.)g Fc(3)p Fj(\(1\),)f(#R9,)g(33pp.) 704 1660 y(h)n(ttp://www2.com)n(binatorics.org/V)-7 b(olume)p 2172 1660 25 4 v 25 w(3/co)n(v)n(er.h)n(tml)515 1768 y(211.)40 b(A.)23 b(Ehrenfeuc)n(h)n(t)f(and)g(J.)h(Mycielski)f([1979],) f(P)n(ositional)g(strategies)g(for)h(mean)g(pa)n(y-)704 1868 y(o\013)27 b(games,)g Fi(Internat.)i(J.)h(Game)h(The)l(ory)36 b Fc(8)p Fj(,)28 b(109{113.)515 1976 y(212.)40 b(N.)30 b(D.)g(Elkies)f([1996],)f(On)i(n)n(um)n(b)r(ers)f(and)g(endgames:)g (com)n(binatorial)f(game)h(the-)704 2076 y(ory)i(in)i(c)n(hess)e (endgames,)g(in:)i Fi(Games)i(of)g(No)f(Chanc)l(e,)h Fj(Pro)r(c.)d(MSRI)g(W)-7 b(orkshop)704 2175 y(on)37 b(Com)n(binatorial)f(Games,)h(July)-7 b(,)38 b(1994,)d(Berk)n(eley)-7 b(,)37 b(CA,)h(MSRI)g(Publ.)f(\(R.)h(J.)704 2275 y(No)n(w)n(ak)n(o)n (wski,)33 b(ed.\),)j(V)-7 b(ol.)36 b(29,)f(Cam)n(bridge)f(Univ)n(ersit) n(y)h(Press,)f(Cam)n(bridge,)h(pp.)704 2374 y(135{150.)515 2482 y(213.)40 b(D.)28 b(Engel)f([1972],)f(DIM:)i(three-dimensional)e (Sim,)i Fi(J.)i(R)l(e)l(cr.)g(Math.)f Fc(5)p Fj(,)e(274{275.)515 2590 y(214.)40 b(R.)21 b(J.)g(Epp)g(and)g(T.)h(S.)f(F)-7 b(erguson)20 b([1980],)g(A)h(note)g(on)g(tak)n(e-a)n(w)n(a)n(y)d (games,)i Fi(Fib)l(onac)l(ci)704 2690 y(Quart.)27 b Fc(18)p Fj(,)g(300{303.)515 2798 y(215.)40 b(R.)30 b(A.)h(Epstein)f([1977],)e Fi(The)l(ory)33 b(of)g(Gambling)h(and)e(Statistial)g(L)l(o)l(gic)5 b Fj(,)31 b(Academic)704 2897 y(Press,)26 b(New)i(Y)-7 b(ork,)27 b(NY.)515 3005 y(216.)40 b(M.)23 b(C.)g(Er)e([1982],)h(A)h (represen)n(tation)e(approac)n(h)f(to)j(the)g(to)n(w)n(er)f(of)g(Hanoi) h(problem,)704 3105 y Fi(Comput.)30 b(J.)e Fc(25)p Fj(,)f(442{447.)515 3213 y(217.)40 b(M.)30 b(C.)g(Er)f([1983],)g(An)h(analysis)f(of)h(the)g (generalized)f(to)n(w)n(ers)f(of)i(Hanoi)g(problem,)704 3313 y Fi(BIT)39 b Fc(23)p Fj(,)28 b(429{435.)515 3421 y(218.)40 b(M.)31 b(C.)g(Er)f([1983],)f(An)i(iterativ)n(e)f(solution)g (to)h(the)g(generalized)f(to)n(w)n(ers)f(of)i(Hanoi)704 3520 y(problem,)c Fi(BIT)40 b Fc(23)p Fj(,)27 b(295{302.)515 3628 y(219.)40 b(M.)28 b(C.)g(Er)f([1984],)f(A)i(generalization)e(of)h (the)i(cyclic)e(to)n(w)n(ers)f(of)i(Hanoi,)f Fi(Intern.)j(J.)704 3728 y(Comput.)g(Math.)f Fc(15)p Fj(,)f(129{140.)515 3836 y(220.)40 b(M.)27 b(C.)f(Er)g([1984],)f(The)i(colour)e(to)n(w)n (ers)g(of)h(Hanoi:)h(a)f(generalization,)e Fi(Comput.)30 b(J.)704 3935 y Fc(27)p Fj(,)d(80{82.)515 4043 y(221.)40 b(M.)35 b(C.)f(Er)g([1984],)e(The)j(cyclic)f(to)n(w)n(ers)f(of)h (Hanoi:)g(a)g(represen)n(tation)f(approac)n(h,)704 4143 y Fi(Comput.)d(J.)e Fc(27)p Fj(,)f(171{175.)515 4251 y(222.)40 b(M.)25 b(C.)h(Er)e([1984],)g(The)h(generalized)f(colour)g (to)n(w)n(ers)f(of)j(Hanoi:)e(an)h(iterativ)n(e)g(algo-)704 4350 y(rithm,)j Fi(Comput.)i(J.)e Fc(27)p Fj(,)f(278{282.)515 4458 y(223.)40 b(M.)h(C.)g(Er)e([1984],)g(The)i(generalized)e(to)n(w)n (ers)g(of)i(Hanoi)f(problem,)g Fi(J.)i(Inform.)704 4558 y(Optim.)30 b(Sci.)e Fc(5)p Fj(,)g(89{94.)515 4666 y(224.)40 b(M.)28 b(C.)g(Er)f([1985],)f(The)i(complexit)n(y)f(of)h(the)g (generalized)e(cyclic)i(to)n(w)n(ers)e(of)i(Hanoi)704 4765 y(problem,)f Fi(J.)j(A)n(lgorithms)35 b Fc(6)p Fj(,)27 b(351{358.)515 4873 y(225.)40 b(M.)30 b(C.)g(Er)f([1987],)g(A)h (general)f(algorithm)f(for)i(\014nding)g(a)g(shortest)f(path)h(b)r(et)n (w)n(een)704 4973 y(t)n(w)n(o)d Fe(n)p Fj(-con\014gurations,)e Fi(Information)31 b(Scienc)l(es)j Fc(42)p Fj(,)28 b(137{141.)p eop %%Page: 19 19 19 18 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(19)515 523 y(226.)40 b(C.)31 b(Erbas,)g(S.)g(Sark)n(eshik)f(and)i(M.)f(M.)h(T)-7 b(anik)31 b([1992],)f(Di\013eren)n(t)i(p)r(ersp)r(ectiv)n(es)f(of)704 623 y(the)25 b Fe(N)9 b Fj(-queens)23 b(problem,)h Fi(Pr)l(o)l(c.)j(A)n (CM)h(Computer)f(Scienc)l(e)g(Conf.,)h Fj(Kansas)23 b(Cit)n(y)-7 b(,)704 722 y(MO.)515 830 y(227.)40 b(C.)35 b(Erbas)f(and)i(M.)f(M.)h (T)-7 b(anik)35 b([1994],)f(P)n(arallel)f(memory)i(allo)r(cation)f(and) i(data)704 930 y(alignmen)n(t)19 b(in)h(SIMD)h(mac)n(hines,)e Fi(Par)l(al)t(lel)24 b(A)n(lgorithms)g(and)f(Applic)l(ations)28 b Fc(4)p Fj(,)20 b(139{)704 1029 y(151,)40 b(preliminary)g(v)n(ersion)f (app)r(eared)h(under)h(the)h(title:)g(Storage)d(sc)n(hemes)i(for)704 1129 y(parallel)28 b(memory)h(systems)g(and)g(the)h Fe(N)9 b Fj(-queens)29 b(problem,)g(in:)h(Pro)r(c.)e(15th)h(Ann.)704 1229 y(Energy)e(T)-7 b(ec)n(h.)28 b(Conf.,)h(Houston,)f(TX,)h(Amer.)g (So)r(c.)f(Mec)n(h.)h(Eng.,)f(V)-7 b(ol.)28 b(43,)g(1992,)704 1328 y(pp.)g(115{120.)515 1436 y(228.)40 b(C.)23 b(Erbas,)e(M.)i(M.)g (T)-7 b(anik)22 b(and)h(Z.)f(Aliy)n(azicioglu)f([1992],)g(Linear)h (conguence)g(equa-)704 1536 y(tions)i(for)f(the)h(solutions)f(of)h(the) g Fe(N)9 b Fj(-queens)23 b(problem,)h Fi(Inform.)j(Pr)l(o)l(c)l(ess.)g (L)l(ett.)c Fc(41)p Fj(,)704 1636 y(301{306.)515 1743 y(229.)40 b(P)-7 b(.)27 b(Erd})-42 b(os)27 b(and)g(J.)h(L.)g(Selfridge) f([1973],)f(On)i(a)f(com)n(binatorial)f(game,)i Fi(J.)h(Combin.)704 1843 y(The)l(ory)38 b Fj(\(Ser.)28 b(A\))g Fc(14)p Fj(,)f(298{301.)515 1951 y(230.)40 b(J.)28 b(Eric)n(kson)e([1996],)g(New)i(toads)g(and)g (frogs)e(results,)i(in:)g Fi(Games)j(of)g(No)f(Chanc)l(e,)704 2051 y Fj(Pro)r(c.)21 b(MSRI)h(W)-7 b(orkshop)21 b(on)g(Com)n (binatorial)g(Games,)g(July)-7 b(,)22 b(1994,)e(Berk)n(eley)-7 b(,)21 b(CA,)704 2150 y(MSRI)i(Publ.)g(\(R.)g(J.)g(No)n(w)n(ak)n(o)n (wski,)d(ed.\),)j(V)-7 b(ol.)23 b(29,)f(Cam)n(bridge)g(Univ)n(ersit)n (y)g(Press,)704 2250 y(Cam)n(bridge,)k(pp.)i(299{310.)515 2358 y(231.)40 b(J.)31 b(Eric)n(kson)f([1996],)g(So)n(wing)h(games,)g (in:)h Fi(Games)i(of)g(No)g(Chanc)l(e,)h Fj(Pro)r(c.)c(MSRI)704 2457 y(W)-7 b(orkshop)20 b(on)i(Com)n(binatorial)e(Games,)h(July)-7 b(,)22 b(1994,)e(Berk)n(eley)-7 b(,)20 b(CA,)i(MSRI)g(Publ.)704 2557 y(\(R.)j(J.)f(No)n(w)n(ak)n(o)n(wski,)d(ed.\),)k(V)-7 b(ol.)25 b(29,)e(Cam)n(bridge)g(Univ)n(ersit)n(y)g(Press,)g(Cam)n (bridge,)704 2657 y(pp.)28 b(287{297.)515 2765 y(232.)40 b(M.)19 b(Eric)n(kson)e(and)i(F.)h(Harary)d([1983],)h(Picasso)f(animal) i(ac)n(hiev)n(emen)n(t)f(games,)g Fi(Bul)t(l.)704 2864 y(Malaysian)32 b(Math.)f(So)l(c.)d Fc(6)p Fj(,)g(37{44.)515 2972 y(233.)40 b(H.)28 b(Eriksson)e([1995],)f(P)n(ebblings,)i Fi(Ele)l(ctr)l(onic)k(J.)e(Combin.)g Fc(2)p Fj(,)f(#R7,)f(18pp.)704 3072 y(h)n(ttp://www.com)n(binatorics.org/V)-7 b(olume)p 2130 3072 25 4 v 26 w(2/co)n(v)n(er.h)n(tml)515 3180 y(234.)40 b(H.)29 b(Eriksson)e(and)i(B.)g(Lindstr\177)-42 b(om)29 b([1995],)e(Twin)j(jumping)f(c)n(hec)n(k)n(ers)e(in)j Fa(Z)-7 b Fj(,)29 b Fi(Eur)l(o-)704 3279 y(p)l(e)l(an)h(J.)g(Combin.)f Fc(16)p Fj(,)e(153{157.)515 3387 y(235.)40 b(K.)31 b(Eriksson)f ([1991],)g(No)i(p)r(olynomial)f(b)r(ound)h(for)g(the)g(c)n(hip)f (\014ring)h(game)f(on)g(di-)704 3487 y(rected)c(graphs,)f Fi(Pr)l(o)l(c.)31 b(A)n(mer.)f(Math.)h(So)l(c.)d Fc(112)p Fj(,)f(1203{1205.)515 3595 y(236.)40 b(K.)26 b(Eriksson)e([1992],)h (Con)n(v)n(ergence)f(of)i(Mozes')g(game)f(of)h(n)n(um)n(b)r(ers,)g Fi(Line)l(ar)j(A)n(lge-)704 3694 y(br)l(a)h(Appl.)f Fc(166)p Fj(,)e(151{165.)515 3802 y(237.)40 b(K.)c(Eriksson)e([1994],)g(No)r(de) j(\014ring)e(games)g(on)h(graphs,)f Fi(Contemp.)j(Math.)g Fc(178)p Fj(,)704 3902 y(117{127.)515 4010 y(238.)i(K.)19 b(Eriksson)f([1994],)f(Reac)n(habilit)n(y)i(is)g(decidable)g(in)h(the)g (n)n(um)n(b)r(ers)f(game,)g Fi(The)l(or)l(et.)704 4110 y(Comput.)30 b(Sci.)h Fj(\(Math)d(Games\))f Fc(131)p Fj(,)g(431{439.)515 4218 y(239.)40 b(K.)21 b(Eriksson)e([1995],)h(The)i (n)n(um)n(b)r(ers)f(game)f(and)h(Co)n(xeter)g(groups,)f Fi(Discr)l(ete)k(Math.)704 4317 y Fc(139)p Fj(,)j(155{166.)515 4425 y(240.)40 b(K.)30 b(Eriksson)f([1996],)g(Chip-\014ring)i(games)e (on)i(m)n(utating)g(graphs,)e Fi(SIAM)j(J.)h(Dis-)704 4525 y(cr)l(ete)c(Math.)g Fc(9)p Fj(,)f(118{128.)515 4633 y(241.)40 b(K.)27 b(Eriksson)e([1996],)h(Strong)h(con)n(v)n (ergence)e(and)i(a)g(game)f(of)i(n)n(um)n(b)r(ers,)f Fi(Eur)l(op)l(e)l(an)704 4732 y(J.)j(Combin.)f Fc(17)p Fj(,)e(379{390.)515 4840 y(242.)40 b(K.)e(Eriksson)f([1996],)g(Strong)h (con)n(v)n(ergence)f(and)h(the)i(p)r(olygon)d(prop)r(ert)n(y)h(of)h(1-) 704 4940 y(pla)n(y)n(er)c(games,)h Fi(Discr)l(ete)j(Math.)f Fc(153)p Fj(,)e(105{122,)e(Pro)r(c.)i(5th)h(Conf.)g(on)g(F)-7 b(ormal)p eop %%Page: 20 20 20 19 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(20)704 523 y(P)n(o)n(w)n(er)25 b(Series)i(and)g(Algebraic)g(Com)n(binatorics)f(\(Florence)h(1993\).) 515 631 y(243.)40 b(J.)d(M.)g(Ettinger)f([2000],)g(A)h(metric)g(for)g (p)r(ositional)f(games,)h Fi(The)l(or)l(et.)i(Comput.)704 731 y(Sci.)30 b Fj(\(Math)e(Games\))g Fc(230)p Fj(,)f(207{219.)515 839 y(244.)40 b(R.)32 b(J.)f(Ev)-5 b(ans)31 b([1974],)f(A)i(winning)g (op)r(ening)f(in)h(rev)n(erse)e(Hex,)h Fi(J.)j(R)l(e)l(cr.)f(Math.)g Fc(7)p Fj(,)704 938 y(189{192.)515 1046 y(245.)40 b(R.)28 b(J.)f(Ev)-5 b(ans)27 b([1975{76],)d(Some)k(v)-5 b(arian)n(ts)26 b(of)i(Hex,)f Fi(J.)j(R)l(e)l(cr.)g(Math.)f Fc(8)p Fj(,)e(120{122.)515 1154 y(246.)40 b(R.)32 b(J.)f(Ev)-5 b(ans)31 b([1979],)f(Silv)n (erman's)g(game)h(on)g(in)n(terv)-5 b(als,)31 b Fi(A)n(mer.)i(Math.)i (Monthly)704 1254 y Fc(86)p Fj(,)27 b(277{281.)515 1362 y(247.)40 b(R.)35 b(J.)g(Ev)-5 b(ans)35 b(and)g(G.)h(A.)f(Heuer)g ([1992],)f(Silv)n(erman's)g(game)g(on)h(discrete)g(sets,)704 1461 y Fi(Line)l(ar)30 b(A)n(lgebr)l(a)g(Appl.)f Fc(166)p Fj(,)e(217{235.)515 1569 y(248.)40 b(S.)30 b(Ev)n(en)f(and)g(R.)h(E.)f (T)-7 b(arjan)29 b([1976],)f(A)i(com)n(binatorial)e(problem)h(whic)n(h) h(is)g(com-)704 1669 y(plete)41 b(in)f(p)r(olynomial)g(space,)g Fi(J.)h(Asso)l(c.)h(Comput.)h(Mach.)f Fc(23)p Fj(,)e(710{719,)d(also) 704 1768 y(app)r(eared)h(in)h(Pro)r(c.)f(7th)h(Ann.)g(A)n(CM)g(Symp.)h (Theory)e(of)h(Computing)f(\(Albu-)704 1868 y(querque,)f(NM,)i(1975\),) d(Asso)r(c.)i(Comput.)g(Mac)n(h.,)g(New)g(Y)-7 b(ork,)38 b(NY,)g(1975,)f(pp.)704 1968 y(66{71.)515 2076 y(249.)j(G.)20 b(Exo)r(o)e([1980-81],)e(A)k(new)f(w)n(a)n(y)f(to)i(pla)n(y)e(Ramsey)h (games,)f Fi(J.)23 b(R)l(e)l(cr.)f(Math.)e Fc(13)p Fj(\(2\),)704 2175 y(111{113.)515 2283 y(250.)40 b(U.)29 b(F)-7 b(aigle,)28 b(W.)h(Kern,)f(H.)h(Kierstead)e(and)i(W.)g(T.)g(T)-7 b(rotter)27 b([1993],)g(On)i(the)g(game)704 2383 y(c)n(hromatic)d(n)n (um)n(b)r(er)i(of)f(some)g(classes)f(of)i(graphs,)e Fi(A)n(rs)j (Combin.)h Fc(35)p Fj(,)d(143{150.)515 2491 y(251.)40 b(U.)f(F)-7 b(aigle,)38 b(W.)i(Kern)e(and)g(J.)h(Kuip)r(ers)f([1998],)f (Computing)i(the)g(n)n(ucleolus)f(of)704 2590 y(min-cost)30 b(spanning)f(tree)h(games)f(is)h(NP-hard,)f Fi(Internat.)j(J.)g(Game)g (The)l(ory)39 b Fc(27)p Fj(,)704 2690 y(443{450.)515 2798 y(252.)h(E.)34 b(F)-7 b(alk)n(ener)33 b([1961],)g Fi(Games)k(A)n(ncient)e(and)i(Mo)l(dern)6 b Fj(,)36 b(Do)n(v)n(er,)d (New)i(Y)-7 b(ork,)33 b(NY.)704 2897 y(\(Published)28 b(previously)e(b)n(y)h(Longmans)g(Green,)g(1897.\).)515 3005 y(253.)40 b(B.-J.)c(F)-7 b(alk)n(o)n(wski)36 b(and)h(L.)g(Sc)n (hmitz)g([1986],)f(A)h(note)g(on)g(the)h(queens')f(problem,)704 3105 y Fi(Inform.)30 b(Pr)l(o)l(c)l(ess.)h(L)l(ett.)c Fc(23)p Fj(,)g(39{46.)515 3213 y(254.)40 b(T.)28 b(F)-7 b(eder)27 b([1990],)f(T)-7 b(o)r(etjes,)28 b Fi(A)n(mer.)h(Math.)j (Monthly)k Fc(97)p Fj(,)27 b(785{794.)515 3321 y(255.)40 b(T.)c(S.)g(F)-7 b(erguson)35 b([1974],)g(On)g(sums)h(of)g(graph)f (games)g(with)i(last)e(pla)n(y)n(er)g(losing,)704 3421 y Fi(Internat.)29 b(J.)h(Game)g(The)l(ory)37 b Fc(3)p Fj(,)27 b(159{167.)515 3528 y(256.)40 b(T.)46 b(S.)h(F)-7 b(erguson)45 b([1984],)f(Mis)n(\022)-39 b(ere)45 b(annihilation)h (games,)f Fi(J.)i(Combin.)h(The)l(ory)704 3628 y Fj(\(Ser.)27 b(A\))i Fc(37)p Fj(,)e(205{230.)515 3736 y(257.)40 b(T.)27 b(S.)h(F)-7 b(erguson)26 b([1989],)f(Who)i(solv)n(ed)f(the)i(secretary) d(problem?,)i Fi(Statistic)l(al)j(Sci-)704 3836 y(enc)l(e)k Fc(4)p Fj(,)27 b(282{296.)515 3944 y(258.)40 b(T.)26 b(S.)f(F)-7 b(erguson)25 b([1992],)f(Mate)h(with)h(bishop)g(and)f (knigh)n(t)g(in)h(kriegspiel,)f Fi(The)l(or)l(et.)704 4043 y(Comput.)30 b(Sci.)h Fj(\(Math)d(Games\))f Fc(96)p Fj(,)g(389{403.)515 4151 y(259.)40 b(T.)i(S.)g(F)-7 b(erguson)40 b([1998],)h(Some)g(c)n(hip)h(transfer)f(games,)g Fi(The)l(or)l(et.)j (Comp.)g(Sci.)704 4251 y Fj(\(Math)28 b(Games\))f Fc(191)p Fj(,)g(157{171.)515 4359 y(260.)40 b(A.)c(S.)g(Fin)n(b)r(o)n(w)g(and)g (B.)g(L.)g(Hartnell)g([1983],)e(A)i(game)f(related)h(to)g(co)n(v)n (ering)d(b)n(y)704 4458 y(stars,)26 b Fi(A)n(rs)k(Combinatoria)36 b Fc(16-A)p Fj(,)27 b(189{198.)515 4566 y(261.)40 b(P)-7 b(.)34 b(C.)g(Fish)n(burn)g(and)g(N.)h(J.)f(A.)g(Sloane)g([1989],)e (The)i(solution)g(to)g(Berlek)-5 b(amp's)704 4666 y(switc)n(hing)27 b(game,)g Fi(Discr)l(ete)j(Math.)f Fc(74)p Fj(,)e(263{290.)515 4774 y(262.)40 b(D.)23 b(C.)g(Fisher)g(and)g(J.)f(Ry)n(an)h([1992],)e (Optimal)i(strategies)e(for)h(a)h(generalized)e(\\scis-)704 4873 y(sors,)26 b(pap)r(er,)h(and)h(stone")f(game,)f Fi(A)n(mer.)k(Math.)h(Monthly)36 b Fc(99)p Fj(,)28 b(935{942.)p eop %%Page: 21 21 21 20 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(21)515 523 y(263.)40 b(D.)35 b(C.)g(Fisher)f(and)g(J.)h(Ry)n(an)f([1995],)f(Probabilities)g(within)i (optimal)g(strategies)704 623 y(for)27 b(tournamen)n(t)g(games,)f Fi(Discr)l(ete)k(Appl.)h(Math.)e Fc(56)p Fj(,)e(87{91.)515 731 y(264.)40 b(D.)28 b(C.)h(Fisher)e(and)h(J.)g(Ry)n(an)f([1995],)g(T) -7 b(ournamen)n(t)27 b(games)g(and)h(p)r(ositiv)n(e)f(tourna-)704 830 y(men)n(ts,)h Fi(J.)h(Gr)l(aph)i(The)l(ory)37 b Fc(19)p Fj(,)27 b(217{236.)515 938 y(265.)40 b(M.)32 b(J.)f(Fisc)n(her)g(and)g (R.)h(N.)g(W)-7 b(righ)n(t)31 b([1990],)f(An)i(application)f(of)h (game-theoretic)704 1038 y(tec)n(hniques)d(to)g(cryptograph)n(y)-7 b(,)26 b Fi(A)l(dvanc)l(es)32 b(in)f(c)l(omputational)h(c)l(omplexity)g (the)l(ory)704 1137 y Fj(\(New)27 b(Brunswic)n(k,)e(NJ,)h(1990\),)f (DIMA)n(CS)i(Ser.)f(Discrete)g(Math.)h(Theoret.)f(Com-)704 1237 y(put.)i(Sci.,,)g(V)-7 b(ol.)28 b(13,)e(pp.)i(99{118.)515 1345 y(266.)40 b(J.)50 b(A.)h(Flanigan)f([1978],)f(Generalized)g(t)n(w) n(o-pile)h(Fib)r(onacci)g(nim,)h Fi(Fib)l(onac)l(ci)704 1445 y(Quart.)27 b Fc(16)p Fj(,)g(459{469.)515 1553 y(267.)40 b(J.)c(A.)h(Flanigan)f([1981],)e(On)j(the)g(distribution)f(of)h (winning)f(mo)n(v)n(es)f(in)i(random)704 1652 y(game)27 b(trees,)g Fi(Bul)t(l.)k(A)n(ustr.)d(Math.)j(So)l(c.)e Fc(24)p Fj(,)e(227{237.)515 1760 y(268.)40 b(J.)32 b(A.)g(Flanigan)f ([1981],)g(Selectiv)n(e)g(sums)h(of)g(lo)r(op)n(y)g(partizan)f(graph)g (games,)g Fi(In-)704 1860 y(ternat.)e(J.)h(Game)h(The)l(ory)36 b Fc(10)p Fj(,)27 b(1{10.)515 1968 y(269.)40 b(J.)30 b(A.)h(Flanigan)f([1982],)f(A)h(complete)h(analysis)e(of)h(blac)n (k-white)g(Hac)n(k)n(endot,)g Fi(In-)704 2067 y(ternat.)f(J.)h(Game)h (The)l(ory)36 b Fc(11)p Fj(,)27 b(21{25.)515 2175 y(270.)40 b(J.)26 b(A.)h(Flanigan)e([1982],)g(One-pile)h(time)h(and)f(size)g(dep) r(enden)n(t)h(tak)n(e-a)n(w)n(a)n(y)c(games,)704 2275 y Fi(Fib)l(onac)l(ci)31 b(Quart.)d Fc(20)p Fj(,)f(51{59.)515 2383 y(271.)40 b(J.)45 b(A.)g(Flanigan)g([1983],)e(Slo)n(w)i(joins)g (of)g(lo)r(op)n(y)f(games,)g Fi(J.)i(Combin.)h(The)l(ory)704 2482 y Fj(\(Ser.)27 b(A\))i Fc(34)p Fj(,)e(46{59.)515 2590 y(272.)40 b(J.)23 b(O.)g(Flynn)h([1973],)e(Lion)h(and)h(man:)f (the)h(b)r(oundary)f(constrain)n(t,)f Fi(SIAM)k(J.)g(Con-)704 2690 y(tr)l(ol)36 b Fc(11)p Fj(,)27 b(397{411.)515 2798 y(273.)40 b(J.)28 b(O.)g(Flynn)g([1974],)f(Lion)g(and)h(man:)g(the)h (general)e(case,)g Fi(SIAM)j(J.)g(Contr)l(ol)37 b Fc(12)p Fj(,)704 2897 y(581{597.)515 3005 y(274.)j(J.)22 b(O.)g(Flynn)g ([1974],)f(Some)g(results)h(on)g(max-min)g(pursuit,)g Fi(SIAM)i(J.)h(Contr)l(ol)31 b Fc(12)p Fj(,)704 3105 y(53{69.)515 3213 y(275.)40 b(L.)35 b(R.)g(F)-7 b(oulds)35 b(and)g(D.)h(G.)f(Johnson)f([1984],)f(An)j(application)e(of)h(graph)f (theory)704 3313 y(and)d(in)n(teger)f(programming:)f(c)n(hessb)r(oard)h (non-attac)n(king)f(puzzles,)i Fi(Math.)j(Mag.)704 3412 y Fc(57)p Fj(,)27 b(95{104.)515 3520 y(276.)40 b(A.)30 b(S.)h(F)-7 b(raenk)n(el)29 b([1974],)f(Com)n(binatorial)h(games)g (with)h(an)g(annihilation)g(rule,)g(in:)704 3620 y Fi(The)43 b(In\015uenc)l(e)d(of)j(Computing)f(on)g(Mathematic)l(al)i(R)l(ese)l (ar)l(ch)d(and)i(Educ)l(ation,)704 3719 y Fj(Pro)r(c.)26 b(Symp.)h(Appl.)h(Math.,)g(\(J.)f(P)-7 b(.)27 b(LaSalle,)f(ed.\),)i(V) -7 b(ol.)27 b(20,)g(Amer.)g(Math.)g(So)r(c.,)704 3819 y(Pro)n(vidence,)f(RI,)h(pp.)h(87{91.)515 3927 y(277.)40 b(A.)22 b(S.)f(F)-7 b(raenk)n(el)21 b([1977],)e(The)j(particles)f(and)g (an)n(tiparticles)f(game,)h Fi(Comput.)k(Math.)704 4027 y(Appl.)k Fc(3)p Fj(,)e(327{328.)515 4134 y(278.)40 b(A.)30 b(S.)g(F)-7 b(raenk)n(el)28 b([1980],)g(F)-7 b(rom)30 b(Nim)g(to)g(Go,)f Fi(A)n(nn.)i(Discr)l(ete)h(Math.)f Fc(6)p Fj(,)e(137{156,)704 4234 y(Pro)r(c.)i(Symp.)i(on)f(Com)n (binatorial)e(Mathematics,)i(Com)n(binatorial)e(Designs)i(and)704 4334 y(Their)22 b(Applications)h(\(J.)g(Sriv)-5 b(asta)n(v)g(a,)22 b(ed.\),)h(Colorado)e(State)i(Univ.,)h(F)-7 b(ort)22 b(Collins,)704 4433 y(CO,)27 b(June)h(1978.)515 4541 y(279.)40 b(A.)c(S.)f(F)-7 b(raenk)n(el)35 b([1981],)f(Planar)f(k)n (ernel)i(and)g(Grundy)h(with)g Fe(d)g Ff(\024)g Fj(3,)f Fe(d)3076 4553 y Fb(out)3214 4541 y Ff(\024)g Fj(2,)704 4641 y Fe(d)747 4653 y Fb(in)839 4641 y Ff(\024)22 b Fj(2)28 b(are)e(NP-complete,)h Fi(Discr)l(ete)j(Appl.)h(Math.)e Fc(3)p Fj(,)e(257{262.)515 4749 y(280.)40 b(A.)23 b(S.)g(F)-7 b(raenk)n(el)21 b([1982],)g(Ho)n(w)h(to)h(b)r(eat)f(y)n(our)g (Wytho\013)h(games')f(opp)r(onen)n(t)g(on)g(three)704 4848 y(fron)n(ts,)27 b Fi(A)n(mer.)j(Math.)h(Monthly)36 b Fc(89)p Fj(,)27 b(353{361.)p eop %%Page: 22 22 22 21 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(22)515 523 y(281.)40 b(A.)31 b(S.)f(F)-7 b(raenk)n(el)30 b([1983],)e(15)i(Researc)n(h)f(problems)g (on)h(games,)g Fi(Discr)l(ete)i(Math.)g Fj(in)704 623 y("Researc)n(h)25 b(Problems")h(section,)h(V)-7 b(ols.)28 b Fc(43-46)p Fj(.)515 731 y(282.)40 b(A.)25 b(S.)h(F)-7 b(raenk)n(el)24 b([1984],)f(Wytho\013)j(games,)e(con)n(tin)n(ued)h (fractions,)f(cedar)h(trees)f(and)704 830 y(Fib)r(onacci)37 b(searc)n(hes,)f Fi(The)l(or)l(et.)41 b(Comput.)e(Sci.)g Fc(29)p Fj(,)e(49{73,)f(an)h(earlier)g(v)n(ersion)704 930 y(app)r(eared)h(in)i(Pro)r(c.)e(10th)h(In)n(ternat.)f(Collo)r(q.)h (on)g(Automata,)g(Languages)e(and)704 1029 y(Programming)21 b(\(J.)i(Diaz,)h(ed.\),)g(V)-7 b(ol.)23 b(154,)g(Barcelona,)e(July)i (1983,)f(Lecture)h(Notes)704 1129 y(in)28 b(Computer)f(Science,)h (Springer)e(V)-7 b(erlag,)27 b(Berlin,)g(1983,)f(pp.)i(203{225,.)515 1237 y(283.)40 b(A.)h(S.)g(F)-7 b(raenk)n(el)40 b([1991],)f(Complexit)n (y)h(of)h(games,)f(in:)h Fi(Combinatorial)k(Games,)704 1337 y Fj(Pro)r(c.)35 b(Symp.)h(Appl.)h(Math.)f(\(R.)g(K.)g(Guy)-7 b(,)36 b(ed.\),)h(V)-7 b(ol.)36 b(43,)f(Amer.)h(Math.)g(So)r(c.,)704 1436 y(Pro)n(vidence,)26 b(RI,)h(pp.)h(111{153.)515 1544 y(284.)40 b(A.)30 b(S.)f(F)-7 b(raenk)n(el)29 b([1994],)e(Ev)n(en)i(k)n (ernels,)f Fi(Ele)l(ctr)l(onic)k(J.)f(Combinatorics)39 b Fc(1)p Fj(,)29 b(#R5,)704 1644 y(13pp.)704 1743 y(h)n(ttp://www.com)n (binatorics.org/V)-7 b(olume)p 2130 1743 25 4 v 26 w(1/co)n(v)n(er.h)n (tml)515 1851 y(285.)40 b(A.)35 b(S.)g(F)-7 b(raenk)n(el)33 b([1994],)g(Recreation)h(and)g(depth)h(in)g(com)n(binatorial)e(games,)h (in:)704 1951 y Fi(The)25 b(Lighter)g(Side)h(of)f(Mathematics,)h Fj(Pro)r(c.)21 b(E.)g(Strens)h(Memorial)e(Conf.)i(on)g(Recr.)704 2051 y(Math.)d(and)g(its)g(History)-7 b(,)18 b(Calgary)-7 b(,)17 b(1986,)g(Sp)r(ectrum)j(Series)e(\(R.)i(K.)e(Guy)h(and)g(R.)g (E.)704 2150 y(W)-7 b(o)r(o)r(dro)n(w,)26 b(eds.\),)h(Math.)g(Asso)r (c.)g(of)g(America,)f(W)-7 b(ashington,)27 b(DC,)g(pp.)g(159{173.)515 2258 y(286.)40 b(A.)34 b(S.)g(F)-7 b(raenk)n(el)33 b([1996],)f (Error-correcting)e(co)r(des)j(deriv)n(ed)g(from)h(com)n(binatorial)704 2358 y(games,)23 b(in:)i Fi(Games)j(of)g(No)f(Chanc)l(e,)h Fj(Pro)r(c.)23 b(MSRI)i(W)-7 b(orkshop)24 b(on)g(Com)n(binatorial)704 2457 y(Games,)35 b(July)-7 b(,)36 b(1994,)e(Berk)n(eley)-7 b(,)34 b(CA,)i(MSRI)g(Publ.)g(\(R.)g(J.)g(No)n(w)n(ak)n(o)n(wski,)d (ed.\),)704 2557 y(V)-7 b(ol.)27 b(29,)g(Cam)n(bridge)g(Univ)n(ersit)n (y)f(Press,)g(Cam)n(bridge,)h(pp.)h(417{431.)515 2665 y(287.)40 b(A.)28 b(S.)g(F)-7 b(raenk)n(el)26 b([1996],)g(Scenic)h (trails)g(ascending)g(from)g(sea-lev)n(el)f(Nim)i(to)f(alpine)704 2765 y(c)n(hess,)h(in:)g Fi(Games)k(of)f(No)g(Chanc)l(e,)h Fj(Pro)r(c.)27 b(MSRI)i(W)-7 b(orkshop)28 b(on)g(Com)n(binatorial)704 2864 y(Games,)35 b(July)-7 b(,)36 b(1994,)e(Berk)n(eley)-7 b(,)34 b(CA,)i(MSRI)g(Publ.)g(\(R.)g(J.)g(No)n(w)n(ak)n(o)n(wski,)d (ed.\),)704 2964 y(V)-7 b(ol.)27 b(29,)g(Cam)n(bridge)g(Univ)n(ersit)n (y)f(Press,)g(Cam)n(bridge,)h(pp.)h(13{42.)515 3072 y(288.)40 b(A.)31 b(S.)g(F)-7 b(raenk)n(el)30 b([1997],)f(Com)n(binatorial)h (game)g(theory)g(foundations)g(applied)h(to)704 3171 y(digraph)20 b(k)n(ernels,)g Fi(Ele)l(ctr)l(onic)k(J.)g(Combinatorics) 30 b Fc(4)p Fj(\(2\),)21 b(#R10,)g(17pp.,)f(Wilf)i(F)-7 b(est-)704 3271 y(sc)n(hrift.)704 3371 y(h)n(ttp://www.com)n (binatorics.org/V)g(olume)p 2130 3371 V 26 w(4/wilfto)r(c.h)n(tml)515 3479 y(289.)40 b(A.)f(S.)g(F)-7 b(raenk)n(el)37 b([1998],)g(Heap)i (games,)e(n)n(umeration)h(systems)g(and)h(sequences,)704 3578 y Fi(A)n(nnals)32 b(of)h(Combinatorics)40 b Fc(2)p Fj(,)30 b(197{210,)e(an)i(earlier)f(v)n(ersion)g(app)r(eared)h(in:)h Fi(F)-6 b(un)704 3678 y(With)27 b(A)n(lgorithms)7 b Fj(,)25 b(V)-7 b(ol.)24 b(4)g(of)h Fi(Pr)l(o)l(c)l(e)l(e)l(dings)i(in)g (Informatics)7 b Fj(,)25 b(Carleton)f(Scien)n(ti\014c,)704 3778 y(Univ)n(ersit)n(y)j(of)g(W)-7 b(aterlo)r(o,)27 b(W)-7 b(aterlo)r(o,)27 b(On)n(t.,)g(pp.)h(99{113.)515 3885 y(290.)40 b(A.)35 b(S.)f(F)-7 b(raenk)n(el)33 b([1998],)g (Multivision:)h(an)g(in)n(tractable)g(impartial)f(game)h(with)g(a)704 3985 y(linear)27 b(winning)g(strategy)-7 b(,)27 b Fi(A)n(mer.)j(Math.)h (Monthly)36 b Fc(105)p Fj(,)27 b(923{928.)515 4093 y(291.)40 b(A.)27 b(S.)h(F)-7 b(raenk)n(el)26 b([1998],)f(Recen)n(t)i(results)g (and)g(questions)f(in)i(com)n(binatorial)d(game)704 4193 y(complexities,)h Fi(Pr)l(o)l(c.)j(A)-8 b(WOCA98)28 b(|)g(Ninth)g(A)n (ustr)l(alasian)g(Workshop)i(on)f(Com-)704 4292 y(binatorial)d(A)n (lgorithms,)f Fj(P)n(erth,)20 b(W)-7 b(estern)22 b(Australia,)e(27{30)f (July)j(\(C.)g(Iliop)r(oulos,)704 4392 y(ed.\),)j(pp.)f(124{146,)d (\014nal)j(v)n(ersion)f(to)h(app)r(ear)f(in)i Fi(The)l(or)l(et.)j (Comput.)f(Sci.)p Fj(,)e(sp)r(ecial)704 4491 y(issue)i(on)g(A)-9 b(W)n(OCA98.)515 4599 y(292.)40 b(A.)c(S.)g(F)-7 b(raenk)n(el)35 b([2000],)f(Arra)n(ys,)g(Numeration)h(systems)g(and)h(games,)f Fi(The)l(or)l(et.)704 4699 y(Comput.)30 b(Sci.,)f Fj(sp)r(ecial)f("F)-7 b(un)27 b(in)h(Algorithms")f(issue,)g(to)g(app)r(ear.)515 4807 y(293.)40 b(A.)24 b(S.)h(F)-7 b(raenk)n(el)23 b([2001],)f(Virus)i (v)n(ersus)f(mankind,)h Fi(Pr)l(o)l(c.)k(2nd)f(Intern.)f(Confer)l(enc)l (e)704 4907 y(on)38 b(Computer)g(Games)g(CG'2000,)p Fj(,)i(Hamamatsu,)c (Japan,)f(Oct.)h(2000,)e(Lecture)704 5006 y(Notes)27 b(in)h(Computer)f(Science,)h(Springer.)p eop %%Page: 23 23 23 22 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(23)515 523 y(294.)40 b(A.)31 b(S.)f(F)-7 b(raenk)n(el)30 b(and)g(I.)g(Borosh)f([1973],)g(A)i (generalization)d(of)j(Wytho\013)6 b('s)31 b(game,)704 623 y Fi(J.)f(Combin.)h(The)l(ory)38 b Fj(\(Ser.)28 b(A\))g Fc(15)p Fj(,)f(175{191.)515 731 y(295.)40 b(A.)d(S.)h(F)-7 b(raenk)n(el,)35 b(M.)j(R.)f(Garey)-7 b(,)36 b(D.)i(S.)f(Johnson,)f(T.) h(Sc)n(haefer)f(and)h(Y.)g(Y)-7 b(esha)704 830 y([1978],)19 b(The)i(complexit)n(y)g(of)g(c)n(hec)n(k)n(ers)d(on)j(an)g Fe(n)5 b Ff(\002)g Fe(n)21 b Fj(b)r(oard)f(|)h(preliminary)f(rep)r (ort,)704 930 y Fi(Pr)l(o)l(c.)25 b(19th)f(A)n(nn.)f(Symp.)i(F)-6 b(oundations)24 b(of)h(Computer)f(Scienc)l(e)30 b Fj(\(Ann)22 b(Arb)r(or,)f(MI,)704 1029 y(Oct.)27 b(1978\),)f(IEEE)h(Computer)g(So)r (c.,)g(Long)g(Beac)n(h,)g(CA,)h(pp.)g(55{64.)515 1137 y(296.)40 b(A.)29 b(S.)g(F)-7 b(raenk)n(el)28 b(and)h(E.)g(Goldsc)n (hmidt)g([1987],)e(Pspace-hardness)f(of)j(some)g(com-)704 1237 y(binatorial)d(games,)h Fi(J.)j(Combin.)h(The)l(ory)38 b Fj(\(Ser.)28 b(A\))g Fc(46)p Fj(,)f(21{38.)515 1345 y(297.)40 b(A.)19 b(S.)h(F)-7 b(raenk)n(el)18 b(and)h(F.)g(Harary)f ([1989],)f(Geo)r(detic)j(con)n(traction)d(games)i(on)f(graphs,)704 1445 y Fi(Internat.)29 b(J.)h(Game)g(The)l(ory)37 b Fc(18)p Fj(,)27 b(327{338.)515 1553 y(298.)40 b(A.)21 b(S.)g(F)-7 b(raenk)n(el)20 b(and)h(H.)g(Herda)g([1980],)e(Nev)n(er)h(rush)h(to)f (b)r(e)i(\014rst)e(in)i(pla)n(ying)e(Nim)n(bi,)704 1652 y Fi(Math.)31 b(Mag.)e Fc(53)p Fj(,)e(21{26.)515 1760 y(299.)40 b(A.)e(S.)f(F)-7 b(raenk)n(el,)37 b(A.)h(Ja\013ra)n(y)-7 b(,)36 b(A.)h(Kotzig)g(and)g(G.)h(Sabidussi)f([1995],)f(Mo)r(dular)704 1860 y(Nim,)28 b Fi(The)l(or)l(et.)j(Comput.)f(Sci.)h Fj(\(Math)d(Games\))f Fc(143)p Fj(,)g(319{333.)515 1968 y(300.)40 b(A.)31 b(S.)g(F)-7 b(raenk)n(el)29 b(and)i(A.)g(Kotzig)e ([1987],)g(P)n(artizan)g(o)r(ctal)h(games:)g(partizan)f(sub-)704 2067 y(traction)e(games,)f Fi(Internat.)k(J.)f(Game)i(The)l(ory)36 b Fc(16)p Fj(,)28 b(145{154.)515 2175 y(301.)40 b(A.)33 b(S.)g(F)-7 b(raenk)n(el)32 b(and)h(D.)g(Lic)n(h)n(tenstein)g([1981],)e (Computing)i(a)f(p)r(erfect)h(strategy)704 2275 y(for)24 b Fe(n)12 b Ff(\002)g Fe(n)23 b Fj(c)n(hess)g(requires)g(time)i(exp)r (onen)n(tial)e(in)i Fe(n)p Fj(,)f Fi(J.)j(Combin.)h(The)l(ory)35 b Fj(\(Ser.)24 b(A\))704 2374 y Fc(31)p Fj(,)g(199{214,)d(preliminary)j (v)n(ersion)f(in)i(Pro)r(c.)e(8th)i(In)n(ternat.)f(Collo)r(q.)g (Automata,)704 2474 y(Languages)d(and)i(Programming)e(\(S.)j(Ev)n(en)e (and)h(O.)g(Kariv,)f(eds.\),)i(V)-7 b(ol.)23 b(115,)f(Acre,)704 2574 y(Israel,)28 b(1981,)g(Lecture)h(Notes)g(in)g(Computer)g(Science,) h(Springer)e(V)-7 b(erlag,)28 b(Berlin,)704 2673 y(pp.)g(278{293.)515 2781 y(302.)40 b(A.)22 b(S.)g(F)-7 b(raenk)n(el,)20 b(M.)i(Lo)r(ebl)f (and)h(J.)f(Ne)l(\024)-37 b(set)l(\024)g(ril)19 b([1988],)h (Epidemiograph)n(y)-7 b(,)20 b(I)r(I.)i(Games)704 2881 y(with)g(a)f(dozing)f(y)n(et)h(winning)h(pla)n(y)n(er,)e Fi(J.)k(Combin.)h(The)l(ory)33 b Fj(\(Ser.)21 b(A\))h Fc(49)p Fj(,)f(129{144.)515 2989 y(303.)40 b(A.)d(S.)h(F)-7 b(raenk)n(el)35 b(and)i(M.)h(Lorb)r(erb)r(om)e([1989],)f(Epidemiograph) n(y)g(with)i(v)-5 b(arious)704 3088 y(gro)n(wth)26 b(functions,)i Fi(Discr)l(ete)i(Appl.)h(Math.)e Fc(25)p Fj(,)e(53{71.)515 3196 y(304.)40 b(A.)24 b(S.)g(F)-7 b(raenk)n(el)22 b(and)h(M.)h(Lorb)r (erb)r(om)e([1991],)g(Nimho\013)i(games,)f Fi(J.)j(Combin.)h(The-)704 3296 y(ory)38 b Fj(\(Ser.)27 b(A\))h Fc(58)p Fj(,)g(1{25.)515 3404 y(305.)40 b(A.)c(S.)h(F)-7 b(raenk)n(el)34 b(and)i(J.)g(Ne)l(\024) -37 b(set)l(\024)g(ril)34 b([1985],)g(Epidemiograph)n(y)-7 b(,)34 b Fi(Paci\014c)39 b(J.)f(Math.)704 3504 y Fc(118)p Fj(,)27 b(369{381.)515 3611 y(306.)40 b(A.)31 b(S.)h(F)-7 b(raenk)n(el)30 b(and)g(M.)i(Ozery)e([1998],)f(Adjoining)i(to)g (Wytho\013)6 b('s)32 b(game)e(its)h Fe(P)12 b Fj(-)704 3711 y(p)r(ositions)27 b(as)g(mo)n(v)n(es,)f Fi(The)l(or)l(et.)31 b(Comput.)g(Sci.)d Fc(205)p Fj(,)f(283{296.)515 3819 y(307.)40 b(A.)32 b(S.)h(F)-7 b(raenk)n(el)31 b(and)h(Y.)h(P)n(erl)e ([1975],)f(Constructions)h(in)i(com)n(binatorial)d(games)704 3919 y(with)35 b(cycles,)f Fi(Col)t(l.)39 b(Math.)e(So)l(c.)g(J\023)-42 b(anos)36 b(Bolyai)46 b Fc(10)p Fj(,)34 b(667{699,)e(Pro)r(c.)i(In)n (ternat.)704 4018 y(Collo)r(q.)28 b(on)g(In\014nite)h(and)g(Finite)g (Sets,)g(V)-7 b(ol.)29 b(2)f(\(A.)h(Ha)5 b(jnal,)29 b(R.)f(Rado)g(and)h (V.)g(T.)704 4118 y(S\023)-42 b(os,)27 b(eds.\))h(Keszthely)-7 b(,)27 b(Hungary)-7 b(,)27 b(1973,)e(North-Holland.)515 4226 y(308.)40 b(A.)28 b(S.)g(F)-7 b(raenk)n(el)27 b(and)h(O.)g(Rahat)f ([1999],)g(In\014nite)h(cyclic)g(impartial)f(games,)g Fi(Pr)l(o)l(c.)704 4325 y(1st)d(Intern.)g(Conf.)i(on)e(Computer)h (Games)g(CG'98,)i(Tsukub)l(a,)e(Jap)l(an,)g(Nov.)g(1998,)704 4425 y Fj(Lecture)d(Notes)h(in)g(Computer)g(Science,)g(V)-7 b(ol.)23 b(1558,)e(Springer,)h(pp.)h(212{221,)d(\014nal)704 4525 y(v)n(ersion)26 b(to)h(app)r(ear)g(in)h Fi(The)l(or)l(et.)j (Comput.)f(Sci.)p Fj(,)f(sp)r(ecial)e(issue)g(on)h(CG'98.)515 4633 y(309.)40 b(A.)31 b(S.)f(F)-7 b(raenk)n(el)29 b(and)i(E.)e(R.)i (Sc)n(heinerman)f([1991],)e(A)j(deletion)f(game)g(on)g(h)n(yp)r(er-)704 4732 y(graphs,)c Fi(Discr)l(ete)k(Appl.)h(Math.)e Fc(30)p Fj(,)e(155{162.)515 4840 y(310.)40 b(A.)26 b(S.)h(F)-7 b(raenk)n(el,)25 b(E.)g(R.)i(Sc)n(heinerman)e(and)h(D.)g(Ullman)h ([1993],)d(Undirected)j(edge)704 4940 y(geograph)n(y)-7 b(,)25 b Fi(The)l(or)l(et.)31 b(Comput.)f(Sci.)h Fj(\(Math)d(Games\))f Fc(112)p Fj(,)g(371{381.)p eop %%Page: 24 24 24 23 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(24)515 523 y(311.)40 b(A.)27 b(S.)h(F)-7 b(raenk)n(el)26 b(and)g(S.)i(Simonson)e([1993],)g(Geograph) n(y)-7 b(,)25 b Fi(The)l(or)l(et.)30 b(Comput.)g(Sci.)704 623 y Fj(\(Math)e(Games\))f Fc(110)p Fj(,)g(197{214.)515 731 y(312.)40 b(A.)e(S.)g(F)-7 b(raenk)n(el)37 b(and)h(U.)g(T)-7 b(assa)37 b([1975],)f(Strategy)h(for)g(a)h(class)f(of)h(games)f(with) 704 830 y(dynamic)27 b(ties,)h Fi(Comput.)i(Math.)h(Appl.)e Fc(1)p Fj(,)f(237{254.)515 938 y(313.)40 b(A.)30 b(S.)g(F)-7 b(raenk)n(el)29 b(and)g(U.)h(T)-7 b(assa)29 b([1982],)f(Strategies)h (for)g(comp)r(ounds)g(of)h(partizan)704 1038 y(games,)c Fi(Math.)31 b(Pr)l(o)l(c.)g(Camb.)g(Phil.)h(So)l(c.)c Fc(92)p Fj(,)f(193{204.)515 1146 y(314.)40 b(A.)32 b(S.)f(F)-7 b(raenk)n(el,)31 b(U.)h(T)-7 b(assa)30 b(and)h(Y.)h(Y)-7 b(esha)31 b([1978],)f(Three)h(annihilation)g(games,)704 1245 y Fi(Math.)g(Mag.)e Fc(51)p Fj(,)e(13{17.)515 1353 y(315.)40 b(A.)33 b(S.)h(F)-7 b(raenk)n(el)32 b(and)h(Y.)h(Y)-7 b(esha)33 b([1976],)e(Theory)i(of)g(annihilation)g(games,)f Fi(Bul)t(l.)704 1453 y(A)n(mer.)e(Math.)h(So)l(c.)d Fc(82)p Fj(,)f(775{777.)515 1561 y(316.)40 b(A.)e(S.)h(F)-7 b(raenk)n(el)37 b(and)h(Y.)h(Y)-7 b(esha)38 b([1979],)e(Complexit)n(y)i(of)g(problems)g (in)g(games,)704 1660 y(graphs)26 b(and)h(algebraic)f(equations,)h Fi(Discr)l(ete)j(Appl.)h(Math.)e Fc(1)p Fj(,)e(15{30.)515 1768 y(317.)40 b(A.)28 b(S.)g(F)-7 b(raenk)n(el)26 b(and)i(Y.)g(Y)-7 b(esha)27 b([1982],)f(Theory)g(of)i(annihilation)f(games)g(|)g(I,)h Fi(J.)704 1868 y(Combin.)j(The)l(ory)39 b Fj(\(Ser.)27 b(B\))h Fc(33)p Fj(,)f(60{86.)515 1976 y(318.)40 b(A.)21 b(S.)g(F)-7 b(raenk)n(el)20 b(and)h(Y.)g(Y)-7 b(esha)20 b([1986],)f(The)i(generalized)f(Sprague{Grundy)f(func-)704 2076 y(tion)g(and)g(its)g(in)n(v)-5 b(ariance)18 b(under)h(certain)f (mappings,)h Fi(J.)i(Combin.)j(The)l(ory)30 b Fj(\(Ser.)19 b(A\))704 2175 y Fc(43)p Fj(,)27 b(165{177.)515 2283 y(319.)40 b(A.)26 b(S.)g(F)-7 b(raenk)n(el)25 b(and)g(D.)i(Zusman)e ([1999],)f(A)i(new)g(heap)f(game,)g Fi(Pr)l(o)l(c.)k(1st)f(Intern.)704 2383 y(Conf.)37 b(on)g(Computer)f(Games)h(CG'98,)i(Tsukub)l(a,)d(Jap)l (an,)h(Nov.)g(1998,)h Fj(Lecture)704 2482 y(Notes)25 b(in)g(Computer)f(Science,)h(V)-7 b(ol.)25 b(1558,)e(Springer,)h(pp.)h (205{211,)d(\014nal)j(v)n(ersion)704 2582 y(to)i(app)r(ear)g(in)h Fi(The)l(or)l(et.)j(Comput.)f(Sci.)p Fj(,)f(sp)r(ecial)e(issue)g(on)h (CG'98.)515 2690 y(320.)40 b(C.)24 b(N.)g(F)-7 b(rangakis)22 b([1981],)h(A)h(bac)n(ktrac)n(king)d(algorithm)i(to)h(generate)f(all)g (k)n(ernels)g(of)704 2790 y(a)k(directed)h(graph,)e Fi(Intern.)j(J.)h (Comput.)h(Math.)e Fc(10)p Fj(,)e(35{41.)515 2897 y(321.)40 b(P)-7 b(.)28 b(F)-7 b(rankl)28 b([1987],)f(Cops)i(and)f(robb)r(ers)g (in)h(graphs)e(with)i(large)e(girth)i(and)f(Ca)n(yley)704 2997 y(graphs,)e Fi(Discr)l(ete)k(Appl.)h(Math.)e Fc(17)p Fj(,)e(301{305.)515 3105 y(322.)40 b(P)-7 b(.)29 b(F)-7 b(rankl)29 b([1987],)g(On)g(a)g(pursuit)h(game)f(on)h(Ca)n(yley)e (graphs,)h Fi(Combinatoric)l(a)38 b Fc(7)p Fj(,)704 3205 y(67{70.)515 3313 y(323.)i(D.)28 b(F)-7 b(remlin)28 b([1973],)e(W)-7 b(ell-founded)28 b(games,)e Fi(Eur)l(eka)35 b Fc(36)p Fj(,)27 b(33{37.)515 3421 y(324.)40 b(G.)35 b(H.)g(F)-7 b(ric)n(k)n(e,)34 b(S.)h(M.)g(Hedetniemi,)h(S.)f(T.)g(Hedetniemi,)h(A.) f(A.)g(McRae,)f(C.)h(K.)704 3520 y(W)-7 b(allis,)27 b(M.)h(S.)g (Jacobson,)e(H.)h(W.)h(Martin)g(and)f(W.)h(D.)g(W)-7 b(eakley)27 b([1995],)f(Com)n(bi-)704 3620 y(natorial)g(problems)h(on)g (c)n(hessb)r(oards:)f(a)h(brief)h(surv)n(ey)-7 b(,)26 b(in:)i Fi(Gr)l(aph)j(The)l(ory,)h(Com-)704 3719 y(binatorics,)43 b(and)f(Applic)l(ations:)48 b Fj(Pro)r(c.)39 b(7th)h(Quadrennial)f(In)n (ternat.)g(Conf.)h(on)704 3819 y(the)30 b(Theory)e(and)h(Applications)h (of)f(Graphs)g(\(Y.)h(Ala)n(vi)f(and)g(A.)h(Sc)n(h)n(w)n(enk,)f (eds.\),)704 3919 y(V)-7 b(ol.)27 b(1,)h(Wiley)-7 b(,)28 b(pp.)g(507{528.)515 4027 y(325.)40 b(W.)24 b(W.)h(F)-7 b(unk)n(en)n(busc)n(h)24 b([1971],)e(SIM)j(as)e(a)h(game)f(of)h(c)n (hance,)g Fi(J.)i(R)l(e)l(cr.)h(Math.)e Fc(4)p Fj(\(4\),)704 4126 y(297{298.)515 4234 y(326.)40 b(Z.)28 b(F)r(\177)-44 b(uredi)27 b(and)1244 4213 y(\023)1234 4234 y(A.)h(Seress)f([1994],)f (Maximal)h(triangle-free)g(graphs)f(with)i(restric-)704 4334 y(tions)f(on)h(the)g(degrees,)e Fi(J.)k(Gr)l(aph)h(The)l(ory)36 b Fc(18)p Fj(,)27 b(11{24.)515 4442 y(327.)40 b(H.)31 b(N.)g(Gab)r(o)n(w)f(and)h(H.)g(H.)g(W)-7 b(estermann)31 b([1992],)e(F)-7 b(orests,)29 b(frames,)i(and)f(games:)704 4541 y(algorithms)c(for)h(matroid)g(sums)g(and)h(applications,)f Fi(A)n(lgorithmic)l(a)35 b Fc(7)p Fj(,)28 b(465{497.)515 4649 y(328.)40 b(D.)26 b(Gale)f([1974],)f(A)i(curious)f(Nim-t)n(yp)r(e) h(game,)e Fi(A)n(mer.)k(Math.)i(Monthly)k Fc(81)p Fj(,)25 b(876{)704 4749 y(879.)515 4857 y(329.)40 b(D.)35 b(Gale)g([1979],)e (The)i(game)f(of)h(Hex)f(and)h(the)g(Brou)n(w)n(er)e(\014xed-p)r(oin)n (t)i(theorem,)704 4956 y Fi(A)n(mer.)30 b(Math.)h(Monthly)36 b Fc(86)p Fj(,)27 b(818{827.)p eop %%Page: 25 25 25 24 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(25)515 523 y(330.)40 b(D.)34 b(Gale)e([1986],)g(Problem)g(1237)f(\(line-dra)n(wing)h(game\),)h Fi(Math.)j(Mag.)f Fc(59)p Fj(,)d(111,)704 623 y(solution)27 b(b)n(y)g(J.)h(Hutc)n(hinson)f(and)h(S.)g(W)-7 b(agon,)26 b Fi(ibid.)k Fc(60)d Fj(\(1987\))f(116.)515 731 y(331.)40 b(D.)20 b(Gale)f(and)h(A.)g(Neyman)f([1982],)f(Nim-t)n(yp)r(e)i(games,) f Fi(Internat.)j(J.)g(Game)h(The)l(ory)704 830 y Fc(11)p Fj(,)k(17{20.)515 938 y(332.)40 b(D.)24 b(Gale)f(and)g(F.)h(M.)g(Stew)n (art)f([1953],)e(In\014nite)j(games)f(with)h(p)r(erfect)g(information,) 704 1038 y Fi(A)n(nn.)33 b(of)i(Math.)g(Stud.)e Fj(\(Con)n(tributions)e (to)h(the)h(Theory)d(of)i(Games\),)g(Princeton)704 1137 y Fc(2)p Fj(\(28\),)27 b(245{266.)515 1245 y(333.)40 b(H.)31 b(Galeana-S\023)-42 b(anc)n(hez)28 b([1982],)g(A)j(coun)n (terexample)e(to)h(a)g(conjecture)g(of)g(Meyniel)704 1345 y(on)d(k)n(ernel-p)r(erfect)g(graphs,)f Fi(Discr)l(ete)k(Math.)f Fc(41)p Fj(,)e(105{107.)515 1453 y(334.)40 b(H.)32 b(Galeana-S\023)-42 b(anc)n(hez)30 b([1986],)h(A)h(theorem)g(ab)r(out)g(a)f(conjecture)h (of)g(Meyniel)g(on)704 1553 y(k)n(ernel-p)r(erfect)26 b(graphs,)h Fi(Discr)l(ete)i(Math.)g Fc(59)p Fj(,)f(35{41.)515 1660 y(335.)40 b(H.)28 b(Galeana-S\023)-42 b(anc)n(hez)25 b([1995],)h Fe(B)1782 1672 y Fd(1)1846 1660 y Fj(and)h Fe(B)2070 1672 y Fd(2)2108 1660 y Fj(-orien)n(table)f(graphs)g(in)h(k)n (ernel)g(theory)-7 b(,)704 1760 y Fi(Discr)l(ete)30 b(Math.)f Fc(143)p Fj(,)e(269{274.)515 1868 y(336.)40 b(H.)26 b(Galeana-S\023)-42 b(anc)n(hez)23 b(and)j(V.)g(Neuman-Lara)e([1984],)g(On)h(k)n(ernels)g (and)h(semik)n(er-)704 1968 y(nels)h(of)h(digraphs,)e Fi(Discr)l(ete)k(Math.)f Fc(48)p Fj(,)e(67{76.)515 2076 y(337.)40 b(H.)24 b(Galeana-S\023)-42 b(anc)n(hez)21 b(and)i(V.)h(Neuman-Lara)e([1994],)f(New)j(extensions)f(of)g(k)n(ernel) 704 2175 y(p)r(erfect)h(digraphs)g(to)g(k)n(ernel)f(imp)r(erfect)i (critical)f(digraphs,)f Fi(Gr)l(aphs)28 b(Combin.)d Fc(10)p Fj(,)704 2275 y(329{336.)515 2383 y(338.)40 b(F.)27 b(Galvin)g([1978],) f(Indeterminacy)g(of)h(p)r(oin)n(t-op)r(en)g(games,)f Fi(Bul)t(l.)k(de)g(l'A)l(c)l(ademie)704 2482 y(Polonaise)i(des)e (Scienc)l(es)37 b Fj(\(Math.)28 b(astr.)f(et)g(ph)n(ys.\))h Fc(26)p Fj(,)f(445{449.)515 2590 y(339.)40 b(F.)33 b(Galvin)g([1985],)e (Stationary)h(strategies)g(in)h(top)r(ological)f(games,)g Fi(Pr)l(o)l(c.)k(Conf.)704 2690 y(on)31 b(in\014nitistic)g(mathematics) 38 b Fj(\(Ly)n(on,)28 b(1984\),)f(Publ.)i(D)n(\023)-39 b(ep.)28 b(Math.)h(Nouv)n(elle)f(S)n(\023)-39 b(er.)704 2790 y(B,)27 b(85{2,)f(Univ.)i(Claude-Bernard,)e(Ly)n(on,)h(pp.)h (41{43.)515 2897 y(340.)40 b(F.)h(Galvin)f([1990],)f(Hyp)r(ergraph)h (games)g(and)g(the)h(c)n(hromatic)f(n)n(um)n(b)r(er,)g(in:)h Fi(A)704 2997 y(T)-6 b(ribute)30 b(to)f(Paul)i(Er)l(d})-42 b(os)7 b Fj(,)28 b(Cam)n(bridge)e(Univ)i(Press,)e(Cam)n(bridge,)h(pp.)h (201{206.)515 3105 y(341.)40 b(F.)d(Galvin,)f(T.)h(Jec)n(h)f(and)h(M.)f (Magidor)f([1978],)g(An)j(ideal)e(game,)g Fi(J.)i(Symb)l(olic)704 3205 y(L)l(o)l(gic)33 b Fc(43)p Fj(,)27 b(284{292.)515 3313 y(342.)40 b(F.)30 b(Galvin)g(and)g(M.)h(Sc)n(heep)r(ers)e([1992],) g(A)h(Ramsey)n(an)f(theorem)g(and)h(an)g(in\014nite)704 3412 y(game,)d Fi(J.)i(Combin.)j(The)l(ory)38 b Fj(\(Ser.)28 b(A\))g Fc(59)p Fj(,)f(125{129.)515 3520 y(343.)40 b(F.)h(Galvin)f(and) h(R.)g(T)-7 b(elg\023)-42 b(arsky)38 b([1986],)h(Stationary)h (strategies)f(in)i(top)r(ological)704 3620 y(games,)26 b Fi(T)-6 b(op)l(olo)l(gy)32 b(Appl.)d Fc(22)p Fj(,)e(51{69.)515 3728 y(344.)40 b(A.)30 b(Gangolli)f(and)h(T.)g(Plam)n(b)r(ec)n(k)e ([1989],)h(A)h(note)g(on)f(p)r(erio)r(dicit)n(y)h(in)g(some)f(o)r(ctal) 704 3827 y(games,)d Fi(Internat.)k(J.)g(Game)g(The)l(ory)37 b Fc(18)p Fj(,)27 b(311{320.)515 3935 y(345.)40 b(T.)27 b(E.)h(Gan)n(tner)e([1988],)g(The)i(game)e(of)i(Quatrainmen)n(t,)e Fi(Math.)31 b(Mag.)e Fc(61)p Fj(,)e(29{34.)515 4043 y(346.)40 b(M.)32 b(Gardner)e([1956],)h Fi(Mathematics,)k(Magic)g(and)f(Mystery)7 b Fj(,)33 b(Do)n(v)n(er,)e(New)h(Y)-7 b(ork,)704 4143 y(NY.)515 4251 y(347.)40 b(M.)24 b(Gardner)f([Jan.)h(1957{Dec.)e (1981],)g(Mathematical)i(Games,)g(a)g(column)g(in)g(Sci-)704 4350 y(en)n(ti\014c)k(American.)515 4458 y(348.)40 b(M.)23 b(Gardner)e([1959],)g Fi(F)-6 b(ads)25 b(and)h(F)-6 b(al)t(lacies)27 b(in)e(the)g(Name)g(of)h(Scienc)l(e)6 b Fj(,)23 b(Do)n(v)n(er,)e(NY.) 515 4566 y(349.)40 b(M.)28 b(Gardner)e([1959],)g Fi(L)l(o)l(gic)31 b(Machines)g(and)f(Diagr)l(ams)7 b Fj(,)29 b(McGra)n(w-Hill,)d(NY.)515 4674 y(350.)40 b(M.)26 b(Gardner)f([1959],)g Fi(Mathematic)l(al)30 b(Puzzles)e(of)i(Sam)e(L)l(oyd)9 b Fj(,)27 b(Do)n(v)n(er,)d(New)j(Y)-7 b(ork,)704 4774 y(NY.)515 4882 y(351.)40 b(M.)27 b(Gardner)f([1960],)f Fi(Mor)l(e)30 b(Mathematic)l(al)h(Puzzles)e(of)h(Sam)g(L)l(oyd)9 b Fj(,)27 b(Do)n(v)n(er,)f(New)704 4981 y(Y)-7 b(ork,)27 b(NY.)p eop %%Page: 26 26 26 25 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(26)515 523 y(352.)40 b(M.)19 b(Gardner)f([1966],)f Fi(Mor)l(e)23 b(Mathematic)l(al)g(Puzzles)f(and)g (Diversions)7 b Fj(,)20 b(Harmonds-)704 623 y(w)n(orth,)i(Middlesex,)h (England)f(\(P)n(enguin)g(Bo)r(oks\),)g(translated)g(in)n(to)h(German:) f Fi(Ma-)704 722 y(thematische)31 b(R\177)-42 b(atsel)30 b(und)f(Pr)l(obleme)p Fj(,)g(View)n(eg,)e(Braunsc)n(h)n(w)n(eig,)e (1964.)515 830 y(353.)40 b(M.)g(Gardner,)f(ed.)i([1967],)d Fi(536)43 b(Puzzles)e(and)h(Curious)g(Pr)l(oblems)7 b Fj(,)41 b(Scribner's,)704 930 y(NY,)30 b(reissue)e(of)i(H.)f(E.)h (Dudeney's)f Fi(Mo)l(dern)j(Puzzles)e Fj(and)f Fi(Puzzles)j(and)g (Curious)704 1029 y(Pr)l(oblems)p Fj(.)515 1137 y(354.)40 b(M.)20 b(Gardner)e([1968],)g Fi(L)l(o)l(gic)24 b(Machines,)h(Diagr)l (ams)e(and)g(Bo)l(ole)l(an)h(A)n(lgebr)l(a)6 b Fj(,)20 b(Do)n(v)n(er,)704 1237 y(NY.)515 1345 y(355.)40 b(M.)c(Gardner)e ([1970],)g Fi(F)-6 b(urther)37 b(Mathematic)l(al)i(Diversions)7 b Fj(,)36 b(Allen)g(and)g(Un)n(win,)704 1445 y(London.)515 1553 y(356.)k(M.)28 b(Gardner)e([1977],)g Fi(Mathematic)l(al)32 b(Magic)f(Show)9 b Fj(,)29 b(Knopf,)e(NY.)515 1660 y(357.)40 b(M.)28 b(Gardner)e([1978],)g Fi(A)n(ha!)31 b(Insight)8 b Fj(,)28 b(F)-7 b(reeman,)27 b(New)h(Y)-7 b(ork,)27 b(NY.)515 1768 y(358.)40 b(M.)28 b(Gardner)e([1979],)g Fi(Mathematic)l(al)32 b(Cir)l(cus)7 b Fj(,)28 b(Knopf,)f(NY.)515 1876 y(359.)40 b(M.)31 b(Gardner)e([1981],)g Fi(Entertaining)k(Scienc)l (e)g(Exp)l(eriments)g(with)g(Everyday)h(Ob-)704 1976 y(jets)7 b Fj(,)28 b(Do)n(v)n(er,)e(NY.)515 2084 y(360.)40 b(M.)28 b(Gardner)e([1981],)g Fi(Scienc)l(e)k(Fiction)h(Puzzle)f(T)-6 b(ales)7 b Fj(,)28 b(P)n(otter.)515 2192 y(361.)40 b(M.)28 b(Gardner)e([1982],)g Fi(A)n(ha!)31 b(Gotcha!)10 b Fj(,)30 b(F)-7 b(reeman,)27 b(New)g(Y)-7 b(ork,)27 b(NY.)515 2300 y(362.)40 b(M.)32 b(Gardner)e([1983],)g Fi(New)j(Mathematic)l(al)j (Diversions)e(fr)l(om)g(Scienti\014c)f(A)n(meri-)704 2399 y(c)l(an)6 b Fj(,)31 b(Univ)n(ersit)n(y)e(of)h(Chicago)f(Press,)g (Chicago,)g(b)r(efore)h(that)g(app)r(eared)f(in)i(1971,)704 2499 y(Simon)d(and)f(Sc)n(h)n(uster,)g(New)h(Y)-7 b(ork,)27 b(NY.)h(First)f(app)r(eared)g(in)h(1966.)515 2607 y(363.)40 b(M.)28 b(Gardner)e([1983],)g Fi(Or)l(der)k(and)g(Surprise)6 b Fj(,)28 b(Prometheus)f(Bo)r(oks,)f(Bu\013alo,)h(NY.)515 2715 y(364.)40 b(M.)e(Gardner)e([1983],)g Fi(Whe)l(els,)k(Life)g(and)g (Other)f(Mathematic)l(al)i(A)n(musements)7 b Fj(,)704 2814 y(F)-7 b(reeman,)27 b(New)h(Y)-7 b(ork,)27 b(NY.)515 2922 y(365.)40 b(M.)28 b(Gardner)e([1984],)g Fi(Co)l(des,)31 b(Ciphers)h(and)e(Se)l(cr)l(et)f(Writing)7 b Fj(,)29 b(Do)n(v)n(er,)d(NY.)515 3030 y(366.)40 b(M.)28 b(Gardner)e([1984],)g Fi(Puzzles)k(fr)l(om)g(Other)g(Worlds)7 b Fj(,)28 b(Random)f(House.)515 3138 y(367.)40 b(M.)28 b(Gardner)e([1984],)g Fi(The)31 b(Magic)g(Numb)l(ers)e(of)i(Dr.)f(Matrix)10 b Fj(,)28 b(Prometheus.)515 3246 y(368.)40 b(M.)25 b(Gardner)f([1984],)g Fi(The)29 b(Sixth)e(Bo)l(ok)i(of)f(Mathematic)l(al)h(Games)7 b Fj(,)26 b(Univ.)g(of)f(Chi-)704 3346 y(cago)h(Press.)g(First)i(app)r (eared)e(in)i(1971,)e(F)-7 b(reeman,)27 b(New)h(Y)-7 b(ork,)27 b(NY.)515 3454 y(369.)40 b(M.)f(Gardner)e([1986],)g Fi(Knotte)l(d)i(Doughnuts)g(and)h(Other)g(Mathematic)l(al)i(Enter-)704 3553 y(tainments)7 b Fj(,)27 b(F)-7 b(reeman,)27 b(New)h(Y)-7 b(ork,)27 b(NY.)515 3661 y(370.)40 b(M.)c(Gardner)f([1987],)g Fi(The)j(Se)l(c)l(ond)g(Scienti\014c)f(A)n(meric)l(an)h(Bo)l(ok)h(of)f (Mathemat-)704 3761 y(ic)l(al)f(Puzzles)f(and)g(Diversions)7 b Fj(,)36 b(Univ)n(ersit)n(y)d(of)h(Chicago)f(Press,)g(Chicago.)g (First)704 3861 y(app)r(eared)27 b(in)g(1961,)f(Simon)i(and)f(Sc)n(h)n (uster,)g(NY.)515 3968 y(371.)40 b(M.)h(Gardner)g([1988],)e Fi(Hexa\015exagons)k(and)g(Other)f(Mathematic)l(al)i(Diversions)7 b Fj(,)704 4068 y(Univ)n(ersit)n(y)31 b(of)g(Chicago)g(Press,)f (Chicago,)h(1988.)e(A)k(\014rst)e(v)n(ersion)f(app)r(eared)h(un-)704 4168 y(der)i(the)h(title)h Fi(The)h(Scienti\014c)g(A)n(meric)l(an)f(Bo) l(ok)i(of)f(Mathematic)l(al)i(Puzzles)d(and)704 4267 y(Diversions)p Fj(,)29 b(Simon)e(&)g(Sc)n(h)n(uster,)g(1959,)f(NY.)515 4375 y(372.)40 b(M.)g(Gardner)f([1988],)g Fi(Perplexing)j(Puzzles)g (and)f(T)-6 b(antalizing)43 b(T)-6 b(e)l(asers)7 b Fj(,)40 b(Do)n(v)n(er,)704 4475 y(NY.)515 4583 y(373.)g(M.)22 b(Gardner)f([1988],)g Fi(R)n(idd)t(les)26 b(of)g(the)f(Sphinx)10 b Fj(,)22 b(Math.)h(Asso)r(c.)f(of)g(America,)g(W)-7 b(ash-)704 4682 y(ington,)27 b(DC.)515 4790 y(374.)40 b(M.)29 b(Gardner)f([1988],)f Fi(Time)32 b(T)-6 b(r)l(avel)32 b(and)g(Other)f(Mathematic)l(al)i(Bewilderments)7 b Fj(,)704 4890 y(F)-7 b(reeman,)27 b(New)h(Y)-7 b(ork,)27 b(NY.)p eop %%Page: 27 27 27 26 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(27)515 523 y(375.)40 b(M.)19 b(Gardner)f([1989],)f Fi(How)23 b(Not)e(to)h(T)-6 b(est)22 b(a)g(Psychic)5 b Fj(,)21 b(Prometheus)d(Bo)r(oks,)f(Bu\013alo,)704 623 y(NY.)515 731 y(376.)40 b(M.)46 b(Gardner)f([1989],)f Fi(Mathematic)l(al)49 b(Carnival)9 b Fj(,)47 b(Math.)f(Asso)r(c.)g(of)g (America,)704 830 y(W)-7 b(ashington,)27 b(DC.)h(First)g(app)r(eared)e (in)i(1975,)e(Knopf,)h(NY.)515 938 y(377.)40 b(M.)24 b(Gardner)e([1990],)g Fi(The)27 b(New)f(A)n(mbidextr)l(ous)g(Universe)6 b Fj(,)24 b(F)-7 b(reeman,)23 b(New)h(Y)-7 b(ork,)704 1038 y(NY.)37 b(First)f(app)r(eared)f(in)i(1964,)e(Basic)g(Bo)r(oks,)g (then)i(in)g(1969,)d(New)j(American)704 1137 y(Library)-7 b(.)515 1245 y(378.)40 b(M.)27 b(Gardner)g([1991],)e Fi(The)31 b(Unexp)l(e)l(cte)l(d)e(Hanging)g(and)h(Other)g(Mathematic)l (al)h(Di-)704 1345 y(versions)7 b Fj(,)29 b(Univ)n(ersit)n(y)e(of)i (Chicago)e(Press.)g(First)h(app)r(eared)g(in)g(1969,)f(Simon)h(and)704 1445 y(Sc)n(h)n(uster,)44 b(NY,)h(translated)f(in)n(to)g(German:)g Fi(L)l(o)l(gik)j(Unterm)d(Galgen)p Fj(,)i(View)n(eg,)704 1544 y(Braunsc)n(h)n(w)n(eig,)25 b(1980.)515 1652 y(379.)40 b(M.)34 b(Gardner)g([1992],)e Fi(F)-6 b(r)l(actal)37 b(Music,)g(Hyp)l(er)l(c)l(ar)l(ds)f(and)g(Mor)l(e)6 b Fj(,)36 b(F)-7 b(reeman,)34 b(New)704 1752 y(Y)-7 b(ork,)27 b(NY.)515 1860 y(380.)40 b(M.)28 b(Gardner)e([1992],)g Fi(On)j(the)h(Wild)h(Side)6 b Fj(,)29 b(Prometheus)d(Bo)r(oks,)g (Bu\013alo,)i(NY.)515 1968 y(381.)40 b(M.)28 b(Gardner)e([1993],)g Fi(The)31 b(Bo)l(ok)g(of)f(Visual)g(Il)t(lusions)7 b Fj(,)29 b(Do)n(v)n(er,)d(NY.)515 2076 y(382.)40 b(M.)27 b(Gardner)g([1997],)e Fi(Penr)l(ose)30 b(Tiles)h(to)e(T)-6 b(r)l(ap)l(do)l(or)31 b(Ciphers)7 b Fj(,)30 b(The)d(Math.)g(Asso)r(c.) 704 2175 y(of)c(America,)g(W)-7 b(ashington,)22 b(DC.)i(First)f(app)r (eared)f(in)h(1989,)f(F)-7 b(reeman,)22 b(New)i(Y)-7 b(ork,)704 2275 y(NY.)28 b(F)-7 b(reeman,)27 b(New)h(Y)-7 b(ork,)27 b(NY.)515 2383 y(383.)40 b(M.)28 b(Gardner)e([1997],)g Fi(The)31 b(L)l(ast)e(R)l(e)l(cr)l(e)l(ations)7 b Fj(,)28 b(Cop)r(ernicus,)f(NY.)515 2491 y(384.)40 b(M.)34 b(R.)f(Garey)g(and)g (D.)h(S.)g(Johnson)f([1979],)e Fi(Computers)36 b(and)g(Intr)l (actability:)g(A)704 2590 y(Guide)i(to)f(the)g(The)l(ory)i(of)f (NP-Completeness)7 b Fj(,)36 b(F)-7 b(reeman,)35 b(San)h(F)-7 b(rancisco,)34 b(Ap-)704 2690 y(p)r(endix)28 b(A8:)f(Games)h(and)f (Puzzles,)g(pp.)h(254-258.)515 2798 y(385.)40 b(R.)f(Gasser)e([1996],)g (Solving)g(nine)i(men's)g(Morris,)e(in:)i Fi(Games)h(of)h(No)e(Chanc)l (e,)704 2897 y Fj(Pro)r(c.)21 b(MSRI)h(W)-7 b(orkshop)21 b(on)g(Com)n(binatorial)g(Games,)g(July)-7 b(,)22 b(1994,)e(Berk)n (eley)-7 b(,)21 b(CA,)704 2997 y(MSRI)i(Publ.)g(\(R.)g(J.)g(No)n(w)n (ak)n(o)n(wski,)d(ed.\),)j(V)-7 b(ol.)23 b(29,)f(Cam)n(bridge)g(Univ)n (ersit)n(y)g(Press,)704 3097 y(Cam)n(bridge,)k(pp.)i(101{114.)515 3205 y(386.)40 b(B.)25 b(Gerla)f([2000],)f(Conditioning)i(a)g(state)g (b)n(y)j( )-27 b(Luk)-5 b(asiewicz)25 b(ev)n(en)n(t:)f(a)h (probabilistic)704 3304 y(approac)n(h)19 b(to)j(Ulam)f(Games,)g Fi(The)l(or)l(et.)k(Comput.)g(Sci.)g Fj(\(Math)d(Games\))f Fc(230)p Fj(,)g(149{)704 3404 y(166.)515 3512 y(387.)40 b(J.)25 b(R.)g(Gilb)r(ert,)h(T.)f(Lengauer)e(and)i(R.)h(E.)e(T)-7 b(arjan)25 b([1980],)e(The)i(p)r(ebbling)h(problem)704 3611 y(is)20 b(complete)h(in)g(p)r(olynomial)f(space,)g Fi(SIAM)j(J.)h(Comput.)d Fc(9)p Fj(,)g(513{524,)c(preliminary)704 3711 y(v)n(ersion)31 b(in)j(Pro)r(c.)e(11th)g(Ann.)i(A)n(CM)f(Symp.)h (Theory)e(of)h(Computing)g(\(A)n(tlan)n(ta,)704 3811 y(GA,)28 b(1979\),)e(Asso)r(c.)h(Comput.)h(Mac)n(h.,)f(New)h(Y)-7 b(ork,)27 b(NY,)h(pp.)g(237{248.)515 3919 y(388.)40 b(J.)35 b(Ginsburg)g([1939],)f(Gauss's)h(arithmetization)g(of)h(the)f(problem)h (of)f(8)g(queens,)704 4018 y Fi(Scripta)30 b(Math.)f Fc(5)p Fj(,)f(63{66.)515 4126 y(389.)40 b(A.)30 b(S.)g(Goldstein)f(and) h(E.)f(M.)h(Reingold)f([1995],)f(The)h(complexit)n(y)g(of)h(pursuit)f (on)704 4226 y(a)e(graph,)g Fi(The)l(or)l(et.)j(Comput.)h(Sci.)f Fj(\(Math)e(Games\))g Fc(143)p Fj(,)f(93{112.)515 4334 y(390.)40 b(E.)34 b(Goles)g([1991],)f(Sand)i(piles,)f(com)n(binatorial) f(games)h(and)g(cellular)g(automata,)704 4433 y Fi(Math.)d(Appl.)e Fc(64)p Fj(,)e(101{121.)515 4541 y(391.)40 b(E.)d(Goles)f(and)h(M.)h (A.)f(Kiwi)g([1993],)f(Games)g(on)h(line)h(graphs)d(and)i(sand)g (piles,)704 4641 y Fi(The)l(or)l(et.)31 b(Comput.)f(Sci.)h Fj(\(Math)d(Games\))f Fc(115)p Fj(,)g(321{349)d(\(0{pla)n(y)n(er)i (game\).)515 4749 y(392.)40 b(E.)27 b(Goles)g(and)g(M.)h(Margenstern)d ([1997],)h(Univ)n(ersalit)n(y)g(of)i(the)f(c)n(hip-\014ring)g(game,)704 4848 y Fi(The)l(or)l(et.)k(Comput.)f(Sci.)h Fj(\(Math)d(Games\))f Fc(172)p Fj(,)g(121{134.)p eop %%Page: 28 28 28 27 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(28)515 523 y(393.)40 b(S.)f(W.)g(Golom)n (b)e([1966],)g(A)i(mathematical)f(in)n(v)n(estigation)f(of)i(games)e (of)i(\\tak)n(e-)704 623 y(a)n(w)n(a)n(y",)25 b Fi(J.)30 b(Combin.)h(The)l(ory)36 b Fc(1)p Fj(,)28 b(443{458.)515 731 y(394.)40 b(S.)19 b(W.)h(Golom)n(b)f([1994],)e Fi(Polyomino)l(es:) 25 b(Puzzles,)e(Patterns,)f(Pr)l(oblems,)i(and)e(Pack-)704 830 y(ings)7 b Fj(,)20 b(Princeton)f(Univ)n(ersit)n(y)g(Press.)f (Original)h(edition:)h Fi(Polyomino)l(es)p Fj(,)i(Scribner's,)704 930 y(NY,)28 b(1965;)e(Allen)i(and)f(Un)n(win,)h(London,)f(1965.)515 1038 y(395.)40 b(D.)35 b(M.)g(Gordon,)e(R.)i(W.)g(Robinson)f(and)g(F.)h (Harary)e([1994],)g(Minim)n(um)i(degree)704 1137 y(games)26 b(for)h(graphs,)g Fi(Discr)l(ete)i(Math.)g Fc(128)p Fj(,)e(151{163.)515 1245 y(396.)40 b(E.)34 b(Gr\177)-42 b(adel)34 b([1990],)g(Domino)g (games)g(and)h(complexit)n(y)-7 b(,)34 b Fi(SIAM)i(J.)h(Comput.)e Fc(19)p Fj(,)704 1345 y(787{804.)515 1453 y(397.)40 b(S.)26 b(B.)f(Gran)n(tham)g([1985],)f(Galvin's)h(\\racing)f(pa)n(wns")g(game)h (and)g(a)g(w)n(ell-ordering)704 1553 y(of)i(trees,)g Fi(Memoirs)32 b(A)n(mer.)d(Math.)i(So)l(c.)e Fc(53)p Fj(\(316\),)d(63)h(pp.)515 1660 y(398.)40 b(R.)f(Greenla)n(w,)e(H.)i (J.)f(Ho)r(o)n(v)n(er)f(and)i(W.)g(L.)f(Ruzzo)g([1995],)f Fi(Limits)j(to)g(Par)l(al)t(lel)704 1760 y(Computation:)23 b Fe(P)12 b Fi(-c)l(ompleteness)23 b(The)l(ory)7 b Fj(,)21 b(Oxford)e(Univ)n(ersit)n(y)f(Press,)g(New)i(Y)-7 b(ork.)515 1868 y(399.)40 b(P)-7 b(.)21 b(M.)g(Grundy)h([1964],)d(Mathematics)i (and)g(Games,)g Fi(Eur)l(eka)28 b Fc(27)p Fj(,)21 b(9{11,)f(originally) 704 1968 y(published:)28 b Fi(ibid.)i Fc(2)d Fj(\(1939\),)f(6{8.)515 2076 y(400.)40 b(P)-7 b(.)22 b(M.)h(Grundy)-7 b(,)23 b(R.)g(S.)g(Scorer)f(and)g(C.)h(A.)g(B.)g(Smith)g([1944],)f(Some)g (binary)g(games,)704 2175 y Fi(Math.)31 b(Gaz.)e Fc(28)p Fj(,)e(96{103.)515 2283 y(401.)40 b(P)-7 b(.)27 b(M.)g(Grundy)g(and)g (C.)g(A.)g(B.)g(Smith)h([1956],)d(Disjunctiv)n(e)j(games)e(with)h(the)g (last)704 2383 y(pla)n(y)n(er)f(losing,)h Fi(Pr)l(o)l(c.)j(Camb.)h (Phil.)h(So)l(c.)c Fc(52)p Fj(,)f(527{533.)515 2491 y(402.)40 b(F.)35 b(Grunfeld)f(and)h(R.)f(C.)h(Bell)f([1975],)f Fi(Games)k(of)f(the)h(World)9 b Fj(,)35 b(Holt,)f(Rinehart)704 2590 y(and)27 b(Winston.)515 2698 y(403.)40 b(C.)23 b(D.)g(Grupp)g ([1976],)e Fi(Br)l(ettspiele-Denkspiele)6 b Fj(,)25 b(Hum)n(b)r(oldt-T) -7 b(asc)n(hen)n(buc)n(h)n(v)n(erlag,)704 2798 y(M)r(\177)-44 b(unc)n(hen.)515 2906 y(404.)40 b(L.)24 b(J.)g(Guibas)g(and)f(A.)i(M.)f (Odlyzk)n(o)f([1981],)f(String)i(o)n(v)n(erlaps,)e(pattern)i(matc)n (hing,)704 3005 y(and)j(non)n(transitiv)n(e)f(games,)h Fi(J.)j(Combin.)h(The)l(ory)39 b Fj(\(Ser.)27 b(A\))h Fc(30)p Fj(,)g(183{208.)515 3113 y(405.)40 b(S.)35 b(Gun)n(ther)f ([1874],)f(Zur)i(mathematisc)n(hen)f(Theorie)g(des)g(Sc)n(hac)n(h)n (bretts,)g Fi(A)n(r)l(ch.)704 3213 y(Math.)d(Physik)38 b Fc(56)p Fj(,)27 b(281{292.)515 3321 y(406.)40 b(R.)23 b(K.)f(Guy)h([1976],)d(P)n(ac)n(king)h([1)p Fe(;)14 b(n)p Fj(])22 b(with)h(solutions)f(of)g Fe(ax)8 b Fj(+)g Fe(by)26 b Fj(=)d Fe(cz)t Fj(;)e(the)i(unit)n(y)g(of)704 3421 y(com)n(binatorics,)e Fi(A)n(tti)j(Conv.)j(Linc)l(ei)f(#17,)h(A)l(c)l (ad.)f(Naz.)f(Linc)l(ei,)i(T)-6 b(omo)26 b(II)13 b Fj(,)23 b(Rome,)704 3520 y(pp.)28 b(173{179.)515 3628 y(407.)40 b(R.)31 b(K.)f(Guy)g([1976],)f(Tw)n(en)n(t)n(y)h(questions)g (concerning)f(Con)n(w)n(a)n(y's)f(sylv)n(er)h(coinage,)704 3728 y Fi(A)n(mer.)h(Math.)h(Monthly)36 b Fc(83)p Fj(,)27 b(634{637.)515 3836 y(408.)40 b(R.)19 b(K.)f(Guy)g([1977],)f(Games)h (are)g(graphs,)f(indeed)i(they)f(are)g(trees,)g Fi(Pr)l(o)l(c.)k(2nd)g (Carib.)704 3935 y(Conf.)31 b(Combin.)g(and)f(Comput.,)h Fj(Letc)n(h)n(w)n(orth)c(Press,)f(Barbados,)f(pp.)j(6{18.)515 4043 y(409.)40 b(R.)30 b(K.)g(Guy)h([1977],)d(She)j(lo)n(v)n(es)e(me,)h (she)g(lo)n(v)n(es)f(me)h(not;)h(relativ)n(es)d(of)j(t)n(w)n(o)e(games) 704 4143 y(of)39 b(Lenstra,)f(Een)g(P)n(ak)g(met)h(een)g(Korte)f(Bro)r (ek)g(\(pap)r(ers)g(presen)n(ted)g(to)h(H.)h(W.)704 4242 y(Lenstra\),)27 b(Mathematisc)n(h)g(Cen)n(trum,)g(Amsterdam.)515 4350 y(410.)40 b(R.)f(K.)f(Guy)h([1978],)d(P)n(artizan)h(and)i (impartial)e(com)n(binatorial)g(games,)h Fi(Col)t(lo)l(q.)704 4450 y(Math.)d(So)l(c.)f(J\023)-42 b(anos)34 b(Bolyai)43 b Fc(18)p Fj(,)31 b(437{461,)e(Pro)r(c.)i(5th)h(Hungar.)f(Conf.)h(Com)n (bin.)704 4550 y(V)-7 b(ol.)31 b(I)f(\(A.)i(Ha)5 b(jnal)30 b(and)h(V.)g(T.)f(S\023)-42 b(os,)31 b(eds.\),)g(Keszthely)-7 b(,)30 b(Hungary)-7 b(,)30 b(1976,)f(North-)704 4649 y(Holland.)515 4757 y(411.)40 b(R.)24 b(K.)f(Guy)g([1979],)f(P)n (artizan)g(Games,)h Fi(Col)t(lo)l(ques)k(Internationaux)f(C.)g(N.)g(R.) g(No.)704 4857 y(260)31 b(|)e(Pr)l(obl)n(\022)-40 b(emes)31 b(Combinatoir)l(es)h(et)d(Th)n(\023)-40 b(eorie)32 b(des)e(Gr)l(aphes)7 b Fj(,)29 b(pp.)f(199{205.)p eop %%Page: 29 29 29 28 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(29)515 523 y(412.)40 b(R.)e(K.)g(Guy)g ([1981],)f(An)n(y)n(one)g(for)g(t)n(w)n(opins?,)h(in:)g Fi(The)j(Mathematic)l(al)g(Gar)l(dner)704 623 y Fj(\(D.)28 b(A.)g(Klarner,)e(ed.\),)i(W)-7 b(adsw)n(orth)27 b(In)n(ternat.,)g (Belmon)n(t,)g(CA,)h(pp.)g(2{15.)515 731 y(413.)40 b(R.)25 b(K.)g(Guy)h([1983],)d(Graphs)i(and)g(games,)f(in:)h Fi(Sele)l(cte)l(d)j(T)-6 b(opics)29 b(in)f(Gr)l(aph)g(The)l(ory)704 830 y Fj(\(L.)i(W.)g(Beinek)n(e)f(and)g(R.)h(J.)f(Wilson,)h(eds.\),)f (V)-7 b(ol.)30 b(2,)f(Academic)h(Press,)e(London,)704 930 y(pp.)g(269{295.)515 1038 y(414.)40 b(R.)20 b(K.)g(Guy)h([1986],)d (John)i(Isb)r(ell's)g(game)f(of)h(b)r(eanstalk)g(and)g(John)g(Con)n(w)n (a)n(y's)e(game)704 1137 y(of)27 b(b)r(eans-don't-talk,)g Fi(Math.)k(Mag.)e Fc(59)p Fj(,)e(259{269.)515 1245 y(415.)40 b(R.)26 b(K.)g(Guy)h([1989],)e Fi(F)-6 b(air)29 b(Game)6 b Fj(,)27 b(COMAP)f(Math.)h(Exploration)d(Series,)i(Arling-)704 1345 y(ton,)h(MA.)515 1453 y(416.)40 b(R.)23 b(K.)f(Guy)h([1990],)d(A)j (guessing)f(game)f(of)i(Bill)g(Sands,)f(and)g(Bernardo)f(Recam\023)-42 b(an's)704 1553 y(Barranca,)25 b Fi(A)n(mer.)30 b(Math.)h(Monthly)36 b Fc(97)p Fj(,)27 b(314{315.)515 1660 y(417.)40 b(R.)g(K.)f(Guy)g ([1991],)f(Mathematics)h(from)g(fun)i(&)e(fun)h(from)f(mathematics;)g (an)704 1760 y(informal)18 b(autobiographical)f(history)h(of)i(com)n (binatorial)d(games,)h(in:)h Fi(Paul)k(Halmos:)704 1860 y(Celebr)l(ating)39 b(50)f(Y)-6 b(e)l(ars)37 b(of)i(Mathematics)44 b Fj(\(J.)37 b(H.)f(Ewing)g(and)f(F.)i(W.)g(Gehring,)704 1959 y(eds.\),)28 b(Springer)e(V)-7 b(erlag,)27 b(New)h(Y)-7 b(ork,)27 b(NY,)h(pp.)g(287{295.)515 2067 y(418.)40 b(R.)32 b(K.)g(Guy)g([1996],)e(Com)n(binatorial)h(games,)g(in:)h Fi(Handb)l(o)l(ok)j(of)f(Combinatorics,)704 2167 y Fj(\(R.)25 b(L.)g(Graham,)e(M.)i(Gr\177)-42 b(otsc)n(hel)24 b(and)g(L.)h(Lo)n (v\023)-42 b(asz,)22 b(eds.\),)j(V)-7 b(ol.)25 b(I)r(I,)g (North-Holland,)704 2267 y(Amsterdam,)i(pp.)h(2117{2162.)515 2374 y(419.)40 b(R.)24 b(K.)g(Guy)g([1996],)f(Impartial)g(Games,)h(in:) g Fi(Games)k(of)f(No)g(Chanc)l(e,)h Fj(Pro)r(c.)23 b(MSRI)704 2474 y(W)-7 b(orkshop)20 b(on)i(Com)n(binatorial)e(Games,)h(July)-7 b(,)22 b(1994,)e(Berk)n(eley)-7 b(,)20 b(CA,)i(MSRI)g(Publ.)704 2574 y(\(R.)j(J.)f(No)n(w)n(ak)n(o)n(wski,)d(ed.\),)k(V)-7 b(ol.)25 b(29,)e(Cam)n(bridge)g(Univ)n(ersit)n(y)g(Press,)g(Cam)n (bridge,)704 2673 y(pp.)39 b(61{78,)d(earlier)h(v)n(ersion)g(in:)i Fi(Combinatorial)j(Games)p Fj(,)d(Pro)r(c.)f(Symp.)g(Appl.)704 2773 y(Math.)27 b(\(R.)h(K.)f(Guy)-7 b(,)28 b(ed.\),)g(V)-7 b(ol.)28 b(43,)e(Amer.)i(Math.)f(So)r(c.,)h(Pro)n(vidence,)d(RI,)j (1991,)704 2873 y(pp.)g(35{55.)515 2980 y(420.)40 b(R.)25 b(K.)f(Guy)h([1996],)d(What)j(is)g(a)f(game?,)g(in:)h Fi(Games)i(of)h(No)f(Chanc)l(e,)h Fj(Pro)r(c.)c(MSRI)704 3080 y(W)-7 b(orkshop)20 b(on)i(Com)n(binatorial)e(Games,)h(July)-7 b(,)22 b(1994,)e(Berk)n(eley)-7 b(,)20 b(CA,)i(MSRI)g(Publ.)704 3180 y(\(R.)j(J.)f(No)n(w)n(ak)n(o)n(wski,)d(ed.\),)k(V)-7 b(ol.)25 b(29,)e(Cam)n(bridge)g(Univ)n(ersit)n(y)g(Press,)g(Cam)n (bridge,)704 3279 y(pp.)39 b(43{60,)d(earlier)h(v)n(ersion)g(in:)i Fi(Combinatorial)j(Games)p Fj(,)d(Pro)r(c.)f(Symp.)g(Appl.)704 3379 y(Math.)27 b(\(R.)h(K.)f(Guy)-7 b(,)28 b(ed.\),)g(V)-7 b(ol.)28 b(43,)e(Amer.)i(Math.)f(So)r(c.,)h(Pro)n(vidence,)d(RI,)j (1991,)704 3479 y(pp.)g(1{21.)515 3587 y(421.)40 b(R.)21 b(K.)g(Guy)h([1996],)d(Unsolv)n(ed)i(problems)g(in)g(com)n(binatorial)f (games,)g(in:)i Fi(Games)i(of)704 3686 y(No)32 b(Chanc)l(e,)i Fj(Pro)r(c.)29 b(MSRI)i(W)-7 b(orkshop)29 b(on)h(Com)n(binatorial)f (Games,)h(July)-7 b(,)30 b(1994,)704 3786 y(Berk)n(eley)-7 b(,)33 b(CA,)h(MSRI)h(Publ.)f(\(R.)h(J.)f(No)n(w)n(ak)n(o)n(wski,)e (ed.\),)j(V)-7 b(ol.)34 b(29,)f(Cam)n(bridge)704 3885 y(Univ)n(ersit)n(y)38 b(Press,)f(Cam)n(bridge,)h(pp.)h(475{491,)d(up)r (date)j(with)h(52)e(problems)g(of)704 3985 y(earlier)31 b(v)n(ersion)h(with)h(37)f(problems,)h(in:)g Fi(Combinatorial)k(Games)p Fj(,)d(Pro)r(c.)e(Symp.)704 4085 y(Appl.)27 b(Math.)g(\(R.)g(K.)f(Guy) -7 b(,)27 b(ed.\),)g(V)-7 b(ol.)26 b(43,)g(Amer.)g(Math.)h(So)r(c.,)f (Pro)n(vidence,)f(RI,)704 4184 y(1991,)h(pp.)i(183{189.)515 4292 y(422.)40 b(R.)21 b(K.)g(Guy)h(and)f(C.)g(A.)h(B.)f(Smith)i ([1956],)c(The)j Fe(G)p Fj(-v)-5 b(alues)20 b(of)i(v)-5 b(arious)20 b(games,)g Fi(Pr)l(o)l(c.)704 4392 y(Camb.)31 b(Phil.)h(So)l(c.)c Fc(52)p Fj(,)f(514{526.)515 4500 y(423.)40 b(R.)33 b(K.)g(Guy)g(and)f(R.)i(E.)e(W)-7 b(o)r(o)r(dro)n(w,) 32 b(eds.)h([1994],)e Fi(The)36 b(Lighter)f(Side)h(of)f(Mathe-)704 4599 y(matics,)h Fj(Pro)r(c.)c(E.)i(Strens)f(Memorial)g(Conf.)g(on)h (Recr.)f(Math.)g(and)h(its)g(History)-7 b(,)704 4699 y(Calgary)g(,)26 b(1986,)f(Sp)r(ectrum)j(Series,)f(Math.)h(Asso)r(c.)f (Amer.,)h(W)-7 b(ashington,)27 b(DC.)515 4807 y(424.)40 b(W.)20 b(Guzic)n(ki)g([1990],)e(Ulam's)i(searc)n(hing)e(game)h(with)i (t)n(w)n(o)e(lies,)h Fi(J.)i(Combin.)i(The)l(ory)704 4907 y Fj(\(Ser.)j(A\))i Fc(54)p Fj(,)e(1{19.)p eop %%Page: 30 30 30 29 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(30)515 523 y(425.)40 b(A.)21 b(Ha)5 b(jnal)21 b(and)g(Z.)g(Nagy)f([1984],)g(Ramsey)g(games,)g Fi(T)-6 b(r)l(ans.)24 b(A)n(meric)l(an)g(Math.)h(So)l(c.)704 623 y Fc(284)p Fj(,)i(815{827.)515 731 y(426.)40 b(D.)31 b(R.)g(Hale)f([1983],)f(A)i(v)-5 b(arian)n(t)29 b(of)i(Nim)g(and)f(a)g (function)h(de\014ned)g(b)n(y)f(Fib)r(onacci)704 830 y(represen)n(tation,)c Fi(Fib)l(onac)l(ci)31 b(Quart.)d Fc(21)p Fj(,)f(139{142.)515 938 y(427.)40 b(A.)f(W.)g(Hales)g(and)g(R.) g(I.)g(Jew)n(ett)f([1963],)g(Regularit)n(y)f(and)i(p)r(ositional)f (games,)704 1038 y Fi(T)-6 b(r)l(ans.)30 b(A)n(mer.)g(Math.)h(So)l(c.)d Fc(106)p Fj(,)f(222{229.)515 1146 y(428.)40 b(L.)34 b(Halp)r(enn)n(y)f (and)h(C.)g(Sm)n(yth)g([1992],)e(A)i(classi\014cation)f(of)g(minimal)h (standard-)704 1245 y(path)25 b(2)13 b Ff(\002)g Fj(2)24 b(switc)n(hing)h(net)n(w)n(orks,)f Fi(The)l(or)l(et.)k(Comput.)g(Sci.)g Fj(\(Math)e(Games\))f Fc(102)p Fj(,)704 1345 y(329{354.)515 1453 y(429.)40 b(Y.)25 b(O.)f(Hamidoune)g([1987],)f(On)h(a)g(pursuit)h (game)e(of)i(Ca)n(yley)e(digraphs,)g Fi(Eur)l(op.)28 b(J.)704 1553 y(Combin.)h Fc(8)p Fj(,)f(289{295.)515 1660 y(430.)40 b(Y.)19 b(O.)f(Hamidoune)g(and)h(M.)g(Las)e(V)-7 b(ergnas)18 b([1985],)e(The)j(directed)f(Shannon)h(switc)n(h-)704 1760 y(ing)34 b(game)f(and)h(the)h(one-w)n(a)n(y)d(game,)h(in:)h Fi(Gr)l(aph)j(The)l(ory)h(and)e(Its)f(Applic)l(ations)704 1860 y(to)k(A)n(lgorithms)h(and)g(Computer)f(Scienc)l(e)45 b Fj(\(Y.)38 b(Ala)n(vi)g(et)g(al.,)f(eds.\),)h(Wiley)-7 b(,)39 b(pp.)704 1959 y(391{400.)515 2067 y(431.)h(Y.)34 b(O.)g(Hamidoune)f(and)h(M.)g(Las)f(V)-7 b(ergnas)33 b([1986],)f(Directed)i(switc)n(hing)f(games)704 2167 y(on)27 b(graphs)f(and)i(matroids,)e Fi(J.)k(Combin.)h(The)l(ory)39 b Fj(\(Ser.)28 b(B\))f Fc(40)p Fj(,)h(237{269.)515 2275 y(432.)40 b(Y.)25 b(O.)g(Hamidoune)g(and)g(M.)g(Las)g(V)-7 b(ergnas)23 b([1987],)h(A)h(solution)g(to)g(the)g(b)r(o)n(x)g(game,)704 2374 y Fi(Discr)l(ete)30 b(Math.)f Fc(65)p Fj(,)e(157{171.)515 2482 y(433.)40 b(Y.)d(O.)f(Hamidoune)g(and)h(M.)g(Las)e(V)-7 b(ergnas)36 b([1988],)e(A)j(solution)f(to)h(the)g(mis)n(\022)-39 b(ere)704 2582 y(Shannon)27 b(switc)n(hing)g(game,)g Fi(Discr)l(ete)j(Math.)f Fc(72)p Fj(,)e(163{166.)515 2690 y(434.)40 b(O.)23 b(Hanner)h([1959],)e(Mean)i(pla)n(y)f(of)h(sums) g(of)f(p)r(ositional)h(games,)f Fi(Paci\014c)k(J.)g(Math.)704 2790 y Fc(9)p Fj(,)g(81{99.)515 2897 y(435.)40 b(F.)24 b(Harary)e([1982],)h(Ac)n(hiev)n(emen)n(t)g(and)h(a)n(v)n(oidance)e (games)h(for)h(graphs,)e Fi(A)n(nn.)k(Dis-)704 2997 y(cr)l(ete)j(Math.) g Fc(13)p Fj(,)f(111{120.)515 3105 y(436.)40 b(F.)24 b(Harary)f(and)h(K.)g(Plo)r(c)n(hinski)f([1987],)g(On)h(degree)f(ac)n (hiev)n(emen)n(t)g(and)h(a)n(v)n(oidance)704 3205 y(games)i(for)h (graphs,)g Fi(Math.)k(Mag.)e Fc(60)p Fj(,)e(316{321.)515 3313 y(437.)40 b(H.)30 b(Harb)r(orth)e(and)h(M.)h(Seemann)f([1996],)e (Snaky)i(is)g(an)g(edge-to-edge)f(loser,)g Fi(Ge-)704 3412 y(ombinatorics)36 b Fc(5)p Fj(,)28 b(132{136.)515 3520 y(438.)40 b(H.)25 b(Harb)r(orth)e(and)h(M.)h(Seemann)f([1997],)e (Snaky)i(is)g(a)g(pa)n(ving)f(winner,)i Fi(Bul)t(l.)i(Inst.)704 3620 y(Combin.)k(Appl.)e Fc(19)p Fj(,)e(71{78.)515 3728 y(439.)40 b(P)-7 b(.)31 b(J.)g(Ha)n(y)n(es)f([1977],)f(A)j(note)f(on)g (the)h(to)n(w)n(ers)e(of)h(Hanoi)g(problem,)f Fi(Computer)k(J.)704 3827 y Fc(20)p Fj(,)27 b(282{285.)515 3935 y(440.)40 b(O.)31 b(Heden)h([1992],)d(On)i(the)h(mo)r(dular)f Fe(n)p Fj(-queen)g(problem,)g Fi(Discr)l(ete)i(Math.)g Fc(102)p Fj(,)704 4035 y(155{161.)515 4143 y(441.)40 b(O.)26 b(Heden)h([1993],)d (Maximal)i(partial)f(spreads)h(and)g(the)g(mo)r(dular)g Fe(n)p Fj(-queen)g(prob-)704 4242 y(lem,)i Fi(Discr)l(ete)h(Math.)g Fc(120)p Fj(,)e(75{91.)515 4350 y(442.)40 b(O.)26 b(Heden)h([1995],)d (Maximal)i(partial)f(spreads)h(and)g(the)g(mo)r(dular)g Fe(n)p Fj(-queen)g(prob-)704 4450 y(lem)i(I)r(I,)g Fi(Discr)l(ete)h (Math.)g Fc(142)p Fj(,)e(97{106.)515 4558 y(443.)40 b(P)-7 b(.)23 b(Hein)g([1942],)e(P)n(olygon,)g Fi(Politiken)34 b Fj(\(description)23 b(of)g(Hex)g(in)g(this)g(Danish)h(news-)704 4658 y(pap)r(er)j(of)h(Dec.)g(26\))e(.)515 4765 y(444.)40 b(D.)34 b(Hensley)f([1988],)f(A)i(winning)g(strategy)e(at)h(T)-7 b(axman,)33 b Fi(Fib)l(onac)l(ci)k(Quart.)c Fc(26)p Fj(,)704 4865 y(262{270.)p eop %%Page: 31 31 31 30 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(31)515 523 y(445.)40 b(C.)26 b(W.)h(Henson)f([1970],)f(Winning)i(strategies)e(for)g(the)i(ideal)f (game,)g Fi(A)n(mer.)j(Math.)704 623 y(Monthly)36 b Fc(77)p Fj(,)27 b(836{840.)515 731 y(446.)40 b(G.)26 b(A.)h(Heuer)f([1982],)e (Odds)i(v)n(ersus)f(ev)n(ens)h(in)g(Silv)n(erman-t)n(yp)r(e)f(games,)g Fi(Internat.)704 830 y(J.)30 b(Game)g(The)l(ory)37 b Fc(11)p Fj(,)27 b(183{194.)515 938 y(447.)40 b(G.)26 b(A.)h(Heuer)e([1989],)g(Reduction)h(of)g(Silv)n(erman-lik)n(e)e(games) h(to)h(games)f(on)h(b)r(oun-)704 1038 y(ded)i(sets,)f Fi(Internat.)i(J.)h(Game)h(The)l(ory)36 b Fc(18)p Fj(,)27 b(31{36.)515 1146 y(448.)40 b(G.)27 b(A.)g(Heuer)g(and)g(U.)g(Leop)r (old-Wildburger)e([1995],)g Fi(Silverman)-8 b('s)30 b(game,)g(A)f(sp)l (e-)704 1245 y(cial)f(class)f(of)h(two-p)l(erson)f(zer)l(o-sum)f (games,)h Fj(with)e(a)f(forew)n(ord)e(b)n(y)i(Reinhard)g(Sel-)704 1345 y(ten,)31 b(V)-7 b(ol.)32 b(424)d(of)38 b(Lecture)31 b(Notes)f(in)i(Economics)e(and)g(Mathematical)h(Systems,)704 1445 y(Springer-V)-7 b(erlag,)25 b(Berlin.)515 1553 y(449.)40 b(G.)23 b(A.)g(Heuer)f(and)g(W.)h(D.)g(Rieder)g([1988],)e(Silv)n(erman) g(games)h(on)g(disjoin)n(t)h(discrete)704 1652 y(sets,)k Fi(SIAM)j(J.)g(Disc.)g(Math.)f Fc(1)p Fj(,)e(485{525.)515 1760 y(450.)40 b(R.)d(Hill)g(and)g(J.)g(P)-7 b(.)36 b(Karim)g([1992],)f (Searc)n(hing)g(with)j(lies:)e(the)i(Ulam)f(problem,)704 1860 y Fi(Discr)l(ete)30 b(Math.)f Fc(106/107)p Fj(,)c(273{283.)515 1968 y(451.)40 b(T.)32 b(P)-7 b(.)31 b(Hill)h(and)g(U.)g(Krengel)e ([1991],)g(Minimax-optimal)h(stop)h(rules)f(and)h(distri-)704 2067 y(butions)27 b(in)h(secretary)e(problems,)h Fi(A)n(nn.)i(Pr)l(ob)l (ab.)g Fc(19)p Fj(,)f(342{353.)515 2175 y(452.)40 b(T.)e(P)-7 b(.)38 b(Hill)h(and)f(U.)h(Krengel)e([1992],)f(On)i(the)h(game)f(of)g (Go)r(ogol,)f Fi(Internat.)i(J.)704 2275 y(Game)30 b(The)l(ory)37 b Fc(21)p Fj(,)27 b(151{160.)515 2383 y(453.)40 b(P)-7 b(.)33 b(G.)h(Hinman)g([1972],)d(Finite)k(termination)e(games)f(with)i (tie,)g Fi(Isr)l(ael)h(J.)h(Math.)704 2482 y Fc(12)p Fj(,)27 b(17{22.)515 2590 y(454.)40 b(A.)25 b(M.)h(Hinz)f([1989],)e(An) j(iterativ)n(e)e(algorithm)g(for)g(the)i(to)n(w)n(er)d(of)i(Hanoi)g (with)g(four)704 2690 y(p)r(egs,)i Fi(Computing)36 b Fc(42)p Fj(,)27 b(133{140.)515 2798 y(455.)40 b(A.)28 b(M.)g(Hinz)g([1989],)e(The)h(to)n(w)n(er)g(of)g(Hanoi,)g Fi(Enseign.)k(Math.)e Fc(35)p Fj(,)e(289{321.)515 2906 y(456.)40 b(A.)28 b(M.)g(Hinz)g([1992],)e(P)n(ascal's)f(triangle)i(and) g(the)h(to)n(w)n(er)e(of)i(Hanoi,)f Fi(A)n(mer.)j(Math.)704 3005 y(Monthly)36 b Fc(99)p Fj(,)27 b(538{544.)515 3113 y(457.)40 b(A.)32 b(M.)g(Hinz)h([1992],)d(Shortest)i(paths)g(b)r(et)n (w)n(een)f(regular)g(states)g(of)h(the)g(to)n(w)n(er)f(of)704 3213 y(Hanoi,)c Fi(Inform.)k(Sci.)d Fc(63)p Fj(,)f(173{181.)515 3321 y(458.)40 b(S.)28 b(Hitotumatu)g([1968],)e(Some)h(remarks)f(on)h (nim-lik)n(e)g(games,)g Fi(Comment.)j(Math.)704 3421 y(Univ.)g(St.)f(Paul)37 b Fc(17)p Fj(,)27 b(85{98.)515 3528 y(459.)40 b(E.)28 b(J.)h(Ho\013man,)g(J.)f(C.)h(Lo)r(essi)f(and)h (R.)g(C.)g(Mo)r(ore)e([1969],)g(Construction)h(for)h(the)704 3628 y(solution)e(of)g(the)h Fe(n)p Fj(-queens)f(problem,)g Fi(Math.)k(Mag.)f Fc(42)p Fj(,)d(66{72.)515 3736 y(460.)40 b(J.)32 b(C.)g(Hollada)n(y)f([1957],)g(Cartesian)g(pro)r(ducts)g(of)i (termination)f(games,)f Fi(A)n(nn.)i(of)704 3836 y(Math.)41 b(Stud.)f Fj(\(Con)n(tributions)f(to)g(the)g(Theory)f(of)i(Games\),)f (Princeton)f Fc(3)p Fj(\(39\),)704 3935 y(189{200.)515 4043 y(461.)i(J.)27 b(C.)h(Hollada)n(y)e([1958],)g(Matrix)h(nim,)h Fi(A)n(mer.)i(Math.)h(Monthly)36 b Fc(65)p Fj(,)27 b(107{109.)515 4151 y(462.)40 b(J.)29 b(C.)g(Hollada)n(y)f([1966],)f(A)j(note)f(on)f (the)i(game)e(of)h(dots,)g Fi(A)n(mer.)i(Math.)i(Monthly)704 4251 y Fc(73)p Fj(,)27 b(717{720.)515 4359 y(463.)40 b(K.)24 b(Igusa)g([1985],)f(Solution)i(of)f(the)h(Bulgarian)e (solitaire)h(conjecture,)g Fi(Math.)k(Mag.)704 4458 y Fc(58)p Fj(,)f(259{271.)515 4566 y(464.)40 b(J.)26 b(Isb)r(ell)g ([1992],)e(The)i(Gordon)f(game)h(of)g(a)f(\014nite)i(group,)e Fi(A)n(mer.)j(Math.)i(Monthly)704 4666 y Fc(99)p Fj(,)d(567{569.)515 4774 y(465.)40 b(O.)27 b(Itzinger)g([1977],)f(The)i(South)g(American)f (game,)f Fi(Math.)32 b(Mag.)d Fc(50)p Fj(,)e(17{21.)515 4882 y(466.)40 b(S.)e(Iw)n(ata)f(and)g(T.)h(Kasai)e([1994],)h(The)g (Othello)h(game)f(on)g(an)h Fe(n)25 b Ff(\002)g Fe(n)37 b Fj(b)r(oard)g(is)704 4981 y(PSP)-7 b(A)n(CE-complete,)26 b Fi(The)l(or)l(et.)31 b(Comput.)f(Sci.)h Fj(\(Math)d(Games\))f Fc(123)p Fj(,)g(329{340.)p eop %%Page: 32 32 32 31 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(32)515 523 y(467.)40 b(T.)c(A.)g (Jenkyns)g(and)g(J.)f(P)-7 b(.)36 b(Ma)n(yb)r(erry)e([1980],)h(The)h (sk)n(eleton)f(of)h(an)g(impartial)704 623 y(game)31 b(and)h(the)h(Nim-function)g(of)f(Mo)r(ore's)f(Nim)2324 635 y Fb(k)2365 623 y Fj(,)h Fi(Internat.)i(J.)g(Game)g(The)l(ory)704 722 y Fc(9)p Fj(,)27 b(51{63.)515 830 y(468.)40 b(T.)32 b(R.)h(Jensen)f(and)g(B.)h(T)-7 b(oft)32 b([1995],)f Fi(Gr)l(aph)36 b(Coloring)g(Pr)l(oblems)7 b Fj(,)33 b(Wiley-In)n(ter-) 704 930 y(science)44 b(Series)h(in)g(Discrete)g(Mathematics)g(and)g (Optimization,)f(Wiley)-7 b(,)46 b(New)704 1029 y(Y)-7 b(ork,)27 b(NY.)515 1137 y(469.)40 b(D.)27 b(S.)g(Johnson)f([1983],)f (The)i(NP-Completeness)e(Column:)i(An)g(Ongoing)f(Guide,)704 1237 y Fi(J.)32 b(A)n(lgorithms)37 b Fc(4)p Fj(,)29 b(397{411)e(\(9th)j (quarterly)e(column)i(\(games\);)f(column)h(started)704 1337 y(in)e(1981\).)515 1445 y(470.)40 b(W.)30 b(W.)g(Johnson)f ([1879],)f(Note)i(on)f(the)h("15")e(puzzle,)i Fi(A)n(mer.)i(J.)f(Math.) g Fc(2)p Fj(,)f(397{)704 1544 y(399.)515 1652 y(471.)40 b(J.)22 b(P)-7 b(.)21 b(Jones)g([1982],)f(Some)i(undecidable)g (determined)g(games,)f Fi(Internat.)j(J.)g(Game)704 1752 y(The)l(ory)36 b Fc(11)p Fj(,)28 b(63{70.)515 1860 y(472.)40 b(J.)31 b(P)-7 b(.)31 b(Jones)f(and)h(A.)g(S.)h(F)-7 b(raenk)n(el)30 b([1995],)f(Complexities)i(of)g(winning)h(strategies) 704 1959 y(in)c(diophan)n(tine)f(games,)g Fi(J.)i(Complexity)37 b Fc(11)p Fj(,)27 b(435{455.)515 2067 y(473.)40 b(M.)22 b(Kac)g([1974],)e(Hugo)i(Steinhaus,)g(a)g(reminiscence)f(and)h(a)g (tribute,)h Fi(A)n(mer.)i(Math.)704 2167 y(Monthly)36 b Fc(81)p Fj(,)27 b(572{581)d(\(p.)29 b(577\).)515 2275 y(474.)40 b(J.)27 b(Kahane)f(and)h(A.)h(S.)g(F)-7 b(raenk)n(el)26 b([1987],)g Fe(k)s Fj(-W)-7 b(elter)27 b(|)g(a)g(generalization)f(of)h (W)-7 b(el-)704 2374 y(ter's)27 b(game,)g Fi(J.)j(Combin.)h(The)l(ory) 38 b Fj(\(Ser.)28 b(A\))g Fc(46)p Fj(,)f(1{20.)515 2482 y(475.)40 b(J.)33 b(Kahn,)g(J.)g(C.)h(Lagarias)c(and)j(H.)h(S.)g (Witsenhausen)f([1987],)f(Single-suit)h(t)n(w)n(o-)704 2582 y(p)r(erson)27 b(card)f(pla)n(y)-7 b(,)27 b Fi(Internat.)j(J.)g (Game)g(The)l(ory)37 b Fc(16)p Fj(,)27 b(291{320.)515 2690 y(476.)40 b(J.)33 b(Kahn,)g(J.)g(C.)h(Lagarias)c(and)j(H.)h(S.)g (Witsenhausen)f([1988],)f(Single-suit)h(t)n(w)n(o-)704 2790 y(p)r(erson)27 b(card)f(pla)n(y)-7 b(,)27 b(I)r(I.)h(Dominance,)g Fi(Or)l(der)37 b Fc(5)p Fj(,)27 b(45{60.)515 2897 y(477.)40 b(J.)28 b(Kahn,)g(J.)g(C.)h(Lagarias)d(and)i(H.)h(S.)g(Witsenhausen)f ([1989],)f(On)h(Lask)n(er's)f(card)704 2997 y(game,)36 b(in:)g Fi(Di\013er)l(ential)j(games)f(and)h(applic)l(ations,)h Fj(Lecture)c(Notes)h(in)f(Con)n(trol)704 3097 y(and)d(Information)g (Sciences)g(\(T.)h(S.)g(Ba)n(\030)-35 b(sar)32 b(and)h(P)-7 b(.)34 b(Bernhard,)e(eds.\),)i(V)-7 b(ol.)33 b(119,)704 3196 y(Springer)26 b(V)-7 b(erlag,)27 b(Berlin,)g(pp.)h(1{8.)515 3304 y(478.)40 b(J.)33 b(Kahn,)g(J.)g(C.)h(Lagarias)c(and)j(H.)h(S.)g (Witsenhausen)f([1989],)f(Single-suit)h(t)n(w)n(o-)704 3404 y(p)r(erson)27 b(card)f(pla)n(y)-7 b(,)27 b(I)r(I)r(I.)i(The)e (mis)n(\022)-39 b(ere)26 b(game,)h Fi(SIAM)j(J.)g(Disc.)g(Math.)f Fc(2)p Fj(,)e(329{343.)515 3512 y(479.)40 b(L.)21 b(Kalm\023)-42 b(ar)19 b([1928],)g(Zur)i(Theorie)f(der)g(abstrakten)g(Spiele,)h Fi(A)l(cta)i(Sci.)i(Math.)f(Univ.)704 3611 y(Sze)l(ge)l(d)36 b Fc(4)p Fj(,)28 b(65{85.)515 3719 y(480.)40 b(B.)24 b(Kaly)n(anasundram)d([1991],)h(On)h(the)i(p)r(o)n(w)n(er)d(of)i(white) g(p)r(ebbles,)h Fi(Combinatoric)l(a)704 3819 y Fc(11)p Fj(,)i(157{171.)515 3927 y(481.)40 b(B.)29 b(Kaly)n(anasundram)d(and)i (G.)h(Sc)n(hnitger)f([1988],)g(On)g(the)h(p)r(o)n(w)n(er)f(of)h(white)g (p)r(eb-)704 4027 y(bles,)39 b Fi(Pr)l(o)l(c.)i(20th)g(A)n(nn.)f(A)n (CM)h(Symp.)g(The)l(ory)h(of)f(Computing)48 b Fj(\(Chicago,)38 b(IL,)704 4126 y(1988\),)26 b(Asso)r(c.)h(Comput.)h(Mac)n(h.,)f(New)h (Y)-7 b(ork,)27 b(NY,)h(pp.)g(258{266.)515 4234 y(482.)40 b(M.)26 b(Kano)e([1983],)f(Cycle)j(games)e(and)h(cycle)g(cut)h(games,)e Fi(Combinatoric)l(a)35 b Fc(3)p Fj(,)25 b(201{)704 4334 y(206.)515 4442 y(483.)40 b(M.)h(Kano)g([1993],)e(An)j(edge-remo)n (ving)d(game)i(on)g(a)g(graph)f(\(a)h(generalization)704 4541 y(of)48 b(Nim)g(and)f(Ka)n(yles\),)g(in:)h Fi(Optimal)h(c)l (ombinatorial)h(structur)l(es)d(on)h(discr)l(ete)704 4641 y(mathematic)l(al)e(mo)l(dels)52 b Fj(\(in)45 b(Japanese,)d(Ky)n (oto,)h(1992\),)f(S)r(\026)-44 b(urik)-5 b(aisekik)n(enky)r(\026)-44 b(usho)704 4741 y(K\026)i(oky)r(\026)e(uroku,)25 b(pp.)j(82{90.)515 4848 y(484.)40 b(M.)32 b(Kano)f([1996],)f(Edge-remo)n(ving)f(games)i (of)h(star)f(t)n(yp)r(e,)i Fi(Discr)l(ete)g(Math.)h Fc(151)p Fj(,)704 4948 y(113{119.)p eop %%Page: 33 33 33 32 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(33)515 523 y(485.)40 b(M.)33 b(Kano,)e(T.)i(Sasaki,)e(H.)j(F)-7 b(ujita)33 b(and)f(S.)h(Hoshi)g ([1993],)e(Life)i(games)e(of)i(Ibadai)704 623 y(t)n(yp)r(e,)39 b(in:)f Fi(Combinatorial)43 b(structur)l(e)38 b(in)i(mathematic)l(al)h (mo)l(dels)47 b Fj(\(in)39 b(Japanese,)704 722 y(Ky)n(oto,)26 b(1993\),)g(S)r(\026)-44 b(urik)-5 b(aisekik)n(enky)r(\026)-44 b(usho)26 b(K\026)-42 b(oky)r(\026)e(uroku,)25 b(pp.)j(108{117.)515 830 y(486.)40 b(R.)c(M.)f(Karp)g(and)g(Y.)h(Zhang)e([1989],)g(On)h (parallel)g(ev)-5 b(aluation)34 b(of)i(game)f(trees,)704 930 y Fi(Pr)l(o)l(c.)30 b(A)n(CM)h(Symp.)f(Par)l(al)t(lel)i(A)n (lgorithms)e(and)h(A)n(r)l(chite)l(ctur)l(es)7 b Fj(,)26 b(pp.)i(409{420.)515 1038 y(487.)40 b(T.)f(Kasai,)e(A.)i(Adac)n(hi)g (and)f(S.)h(Iw)n(ata)f([1979],)f(Classes)h(of)g(p)r(ebble)i(games)d (and)704 1137 y(complete)27 b(problems,)g Fi(SIAM)j(J.)g(Comput.)e Fc(8)p Fj(,)f(574{586.)515 1245 y(488.)40 b(Y.)25 b(Ka)n(w)n(ano)d ([1996],)h(Using)h(similar)g(p)r(ositions)g(to)h(searc)n(h)e(game)g (trees,)h(in:)h Fi(Games)704 1345 y(of)f(No)e(Chanc)l(e,)j Fj(Pro)r(c.)19 b(MSRI)h(W)-7 b(orkshop)19 b(on)h(Com)n(binatorial)e (Games,)i(July)-7 b(,)20 b(1994,)704 1445 y(Berk)n(eley)-7 b(,)33 b(CA,)h(MSRI)h(Publ.)f(\(R.)h(J.)f(No)n(w)n(ak)n(o)n(wski,)e (ed.\),)j(V)-7 b(ol.)34 b(29,)f(Cam)n(bridge)704 1544 y(Univ)n(ersit)n(y)27 b(Press,)f(Cam)n(bridge,)g(pp.)i(193{202.)515 1652 y(489.)40 b(J.)24 b(C.)h(Ken)n(y)n(on)e([1967],)f(A)j(Nim-lik)n(e) f(game)g(with)h(p)r(erio)r(d)f(349,)f(Res.)i(P)n(ap)r(er)e(No.)h(13,) 704 1752 y(Univ.)k(of)f(Calgary)-7 b(,)26 b(Math.)i(Dept.)515 1860 y(490.)40 b(J.)i(C.)g(Ken)n(y)n(on)e([1967],)g(Nim-lik)n(e)i (games)f(and)g(the)i(Sprague{Grundy)d(theory)-7 b(,)704 1959 y(M.Sc.)28 b(Thesis,)f(Univ.)h(of)g(Calgary)-7 b(.)515 2067 y(491.)40 b(B.)35 b(Kerst)e([1933],)g Fi(Mathematische)39 b(Spiele)6 b Fj(,)36 b(Reprin)n(ted)f(b)n(y)f(Dr.)h(Martin)g(S})-42 b(andig)704 2167 y(oHG,)28 b(Wiesbaden)f(1968.)515 2275 y(492.)40 b(H.)30 b(A.)f(Kierstead)f(and)h(W.)h(T.)f(T)-7 b(rotter)29 b([1994],)e(Planar)h(graph)g(coloring)g(with)h(an)704 2374 y(unco)r(op)r(erativ)n(e)d(partner,)h Fi(J.)j(Gr)l(aph)h(The)l (ory)36 b Fc(18)p Fj(,)27 b(569{584.)515 2482 y(493.)40 b(Y.)31 b(Kim)f([1996],)f(New)h(v)-5 b(alues)30 b(in)h(domineering,)e Fi(The)l(or)l(et.)34 b(Comput.)f(Sci.)g Fj(\(Math)704 2582 y(Games\))27 b Fc(156)p Fj(,)g(263{280.)515 2690 y(494.)40 b(H.)22 b(Kinder)g([1973],)e(Gewinnstrategien)h(des)h (Anziehenden)h(in)f(einigen)g(Spielen)g(auf)704 2790 y(Graphen,)27 b Fi(A)n(r)l(ch.)j(Math.)f Fc(24)p Fj(,)e(332{336.)515 2897 y(495.)40 b(M.)35 b(A.)h(Kiwi,)e(R.)i(Ndoundam,)f(M.)g(Tc)n(h)n (uen)n(te)f(and)h(E.)g(Goles)f([1994],)g(No)h(p)r(oly-)704 2997 y(nomial)g(b)r(ound)h(for)f(the)h(p)r(erio)r(d)f(of)h(the)g (parallel)e(c)n(hip)h(\014ring)g(game)g(on)g(graphs,)704 3097 y Fi(The)l(or)l(et.)c(Comput.)f(Sci.)f Fc(136)p Fj(,)e(527{532.)515 3205 y(496.)40 b(D.)28 b(A.)f(Klarner,)f(ed.)h ([1998],)f Fi(Mathematic)l(al)32 b(r)l(e)l(cr)l(e)l(ations.)e(A)f(c)l (ol)t(le)l(ction)h(in)g(honor)704 3304 y(of)i(Martin)g(Gar)l(dner)9 b Fj(,)31 b(Do)n(v)n(er,)d(Mineola,)h(NY,)h(Corrected)e(reprin)n(t)h (of)h Fi(The)i(Math-)704 3404 y(ematic)l(al)f(Gar)l(dner)p Fj(,)d(W)-7 b(adsw)n(orth)27 b(In)n(ternat.,)g(Belmon)n(t,)g(CA,)h (1981.)515 3512 y(497.)40 b(M.)c(M.)f(Kla)n(w)n(e)f([1985],)g(A)i(tigh) n(t)g(b)r(ound)g(for)f(blac)n(k)f(and)i(white)g(p)r(ebbles)f(on)h(the) 704 3611 y(p)n(yramids,)26 b Fi(J.)k(Asso)l(c.)g(Comput.)h(Mach.)e Fc(32)p Fj(,)f(218{228.)515 3719 y(498.)40 b(C.)c(S.)g(Klein)g(and)f (S.)h(Minsk)n(er)f([1993],)f(The)i(sup)r(er)g(to)n(w)n(ers)e(of)i (Hanoi)g(problem:)704 3819 y(large)26 b(rings)h(on)g(small)g(rings,)g Fi(Discr)l(ete)j(Math.)f Fc(114)p Fj(,)e(283{295.)515 3927 y(499.)40 b(D.)32 b(J.)g(Kleitman)f(and)h(B.)g(L.)g(Rothsc)n(hild) f([1972],)g(A)h(generalization)e(of)h(Kaplan-)704 4027 y(sky's)c(game,)g Fi(Discr)l(ete)i(Math.)g Fc(2)p Fj(,)f(173{178.)515 4134 y(500.)40 b(T.)30 b(Kl\034ve)f([1977],)g(The)h(mo)r(dular)f Fe(n)p Fj(-queen)h(problem,)g Fi(Discr)l(ete)i(Math.)f Fc(19)p Fj(,)f(289{)704 4234 y(291.)515 4342 y(501.)40 b(T.)25 b(Kl\034ve)g([1981],)f(The)h(mo)r(dular)g Fe(n)p Fj(-queen)g(problem)g(I)r(I,)h Fi(Discr)l(ete)h(Math.)g Fc(36)p Fj(,)e(33{)704 4442 y(48.)515 4550 y(502.)40 b(M.)25 b(Knor)e([1996],)g(On)i(Ramsey-t)n(yp)r(e)e(games)h(for)g (graphs,)f Fi(A)n(ustr)l(alas.)k(J.)g(Combin.)704 4649 y Fc(14)p Fj(,)g(199{206.)515 4757 y(503.)40 b(D.)28 b(E.)f(Kn)n(uth)h([1974],)e Fi(Surr)l(e)l(al)j(Numb)l(ers)7 b Fj(,)27 b(Addison-W)-7 b(esley)g(,)27 b(Reading,)g(MA.)515 4865 y(504.)40 b(D.)25 b(E.)f(Kn)n(uth)h([1976],)e(The)i(computer)f(as) g(Master)g(Mind,)i Fi(J.)h(R)l(e)l(cr.)g(Math.)f Fc(9)p Fj(,)e(1{6.)515 4973 y(505.)40 b(D.)23 b(E.)e(Kn)n(uth)h([1977],)f(Are) h(to)n(y)f(problems)h(useful?,)h Fi(Popular)j(Computing)k Fc(5)p Fj(,)22 b(3{10.)p eop %%Page: 34 34 34 33 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(34)515 523 y(506.)40 b(D.)31 b(E.)f(Kn)n(uth)h([1993],)d Fi(The)34 b(Stanfor)l(d)f(Gr)l(aph)g(Base)p Fj(:)f(A)f(Platform)e(for)h(Com)n(bina-)704 623 y(torial)c(Computing)q (,)i(A)n(CM)g(Press,)e(New)i(Y)-7 b(ork.)515 731 y(507.)40 b(P)-7 b(.)35 b(Komj\023)-42 b(ath)35 b([1984],)e(A)j(simple)f (strategy)f(for)h(the)h(Ramsey-game,)d Fi(Studia)k(Sci.)704 830 y(Math.)31 b(Hung.)c Fc(19)p Fj(,)g(231{232.)515 938 y(508.)40 b(A.)31 b(Kotzig)e([1946],)g(O)h Fe(k)s Fj(-p)r(osun)n(utiac)n(h)g(\(On)g Fe(k)s Fj(-translations;)f(in)i(Slo)n (v)-5 b(akian\),)3261 917 y Fi(\024)3247 938 y(Ca-)704 1038 y(sop.)39 b(pr)l(o)g(P)n(\024)-40 b(est.)38 b(Mat.)h(a)f(Fys.)g Fc(71)p Fj(,)e(55{61,)e(extended)j(abstract)f(in)g(F)-7 b(renc)n(h,)37 b(pp.)704 1137 y(62{66.)515 1245 y(509.)j(G.)28 b(Ko)n(w)n(alewski)d([1930],)h Fi(A)n(lte)k(und)f(neue)h(mathematische) h(Spiele)6 b Fj(,)30 b(Reprin)n(ted)d(b)n(y)704 1345 y(Dr.)h(Martin)f(S})-42 b(andig)27 b(oHG,)h(Wiesbaden)f(1968.)515 1453 y(510.)40 b(K.)d(Ko)n(y)n(ama)e(and)i(T.)h(W.)g(Lai)f([1993],)e (An)j(optimal)g(Mastermind)f(strategy)-7 b(,)36 b Fi(J.)704 1553 y(R)l(e)l(cr.)29 b(Math.)g Fc(25)p Fj(,)f(251{256.)515 1660 y(511.)40 b(M.)22 b(Kraitc)n(hik)e([1953],)g Fi(Mathematic)l(al)26 b(R)l(e)l(cr)l(e)l(ations)7 b Fj(,)22 b(Do)n(v)n(er,)e(New)i(Y)-7 b(ork,)21 b(NY,)h(2nd)704 1760 y(edn.)515 1868 y(512.)40 b(B.)45 b(Kummer)h([1980],)e Fi(Spiele)j(auf)g(Gr)l(aphen)6 b Fj(,)48 b(In)n(ternat.)d(Series)g(of)g(Numerical)704 1968 y(Mathematics,)27 b(Birkh\177)-42 b(auser)26 b(V)-7 b(erlag,)27 b(Basel.)515 2076 y(513.)40 b(R.)c(E.)f(Ladner)f(and)i(J.)f (K.)g(Norman)g([1985],)f(Solitaire)h(automata,)f Fi(J.)j(Comput.)704 2175 y(System)29 b(Sci.)g Fc(30)p Fj(,)e(116{129.)515 2283 y(514.)40 b(J.)34 b(C.)g(Lagarias)d([1977],)h(Discrete)i (balancing)f(games,)g Fi(Bul)t(l.)j(Inst.)f(Math.)i(A)l(c)l(ad.)704 2383 y(Sinic)l(a)e Fc(5)p Fj(,)27 b(363{373.)515 2491 y(515.)40 b(S.)26 b(P)-7 b(.)25 b(Lalley)g([1988],)f(A)i (one-dimensional)e(in\014ltration)h(game,)g Fi(Naval)k(R)l(es.)f(L)l(o) l(gis-)704 2590 y(tics)35 b Fc(35)p Fj(,)27 b(441{446.)515 2698 y(516.)40 b(H.)31 b(A.)h(Landman)f([1996],)e(Ey)n(espace)g(v)-5 b(alues)31 b(in)g(Go,)g(in:)h Fi(Games)i(of)f(No)g(Chanc)l(e,)704 2798 y Fj(Pro)r(c.)21 b(MSRI)h(W)-7 b(orkshop)21 b(on)g(Com)n (binatorial)g(Games,)g(July)-7 b(,)22 b(1994,)e(Berk)n(eley)-7 b(,)21 b(CA,)704 2897 y(MSRI)i(Publ.)g(\(R.)g(J.)g(No)n(w)n(ak)n(o)n (wski,)d(ed.\),)j(V)-7 b(ol.)23 b(29,)f(Cam)n(bridge)g(Univ)n(ersit)n (y)g(Press,)704 2997 y(Cam)n(bridge,)k(pp.)i(227{257.)515 3105 y(517.)40 b(L.)28 b(Larson)f([1977],)f(A)i(theorem)g(ab)r(out)g (primes)g(pro)n(v)n(ed)f(on)g(a)h(c)n(hessb)r(oard,)f Fi(Math.)704 3205 y(Mag.)i Fc(50)p Fj(,)e(69{74.)515 3313 y(518.)40 b(E.)23 b(Lask)n(er)f([1931],)h Fi(Br)l(ettspiele)k(der) g(V\177)-42 b(olker,)27 b(R\177)-42 b(atsel)27 b(und)f(mathematische)i (Spiele)6 b Fj(,)704 3412 y(Berlin.)515 3520 y(519.)40 b(I.)28 b(La)n(v)-5 b(al)n(\023)-39 b(ee)26 b([1985],)g(Note)i(sur)g (le)g(probl)n(\022)-39 b(eme)27 b(des)g(tours)h(d'Hano)-9 b(\177)-32 b(\020,)27 b Fi(R)l(ev.)j(R)l(oumaine)704 3620 y(Math.)h(Pur)l(es)e(Appl.)g Fc(30)p Fj(,)f(433{438.)515 3728 y(520.)40 b(E.)21 b(L.)h(La)n(wler)e(and)h(S.)h(Sarkissian)e ([1995],)g(An)i(algorithm)e(for)h(\\Ulam's)g(game")f(and)704 3827 y(its)27 b(application)f(to)h(error)e(correcting)g(co)r(des,)i Fi(Inform.)j(Pr)l(o)l(c)l(ess.)g(L)l(ett.)d Fc(56)p Fj(,)f(89{93.)515 3935 y(521.)40 b(A.)33 b(J.)g(Lazarus,)f(D.)h(E.)g(Lo)r(eb,)g(J.)g(G.)g (Propp)f(and)h(D.)h(Ullman)f([1996],)e(Ric)n(hman)704 4035 y(Games,)22 b(in:)g Fi(Games)j(of)h(No)f(Chanc)l(e,)h Fj(Pro)r(c.)21 b(MSRI)h(W)-7 b(orkshop)21 b(on)h(Com)n(binatorial)704 4134 y(Games,)35 b(July)-7 b(,)36 b(1994,)e(Berk)n(eley)-7 b(,)34 b(CA,)i(MSRI)g(Publ.)g(\(R.)g(J.)g(No)n(w)n(ak)n(o)n(wski,)d (ed.\),)704 4234 y(V)-7 b(ol.)27 b(29,)g(Cam)n(bridge)g(Univ)n(ersit)n (y)f(Press,)g(Cam)n(bridge,)h(pp.)h(439{449.)515 4342 y(522.)40 b(A.)27 b(J.)f(Lazarus,)f(D.)i(E.)f(Lo)r(eb,)h(J.)f(G.)h (Propp,)e(W.)i(R.)g(Stromquist)f(and)h(D.)g(Ullman)704 4442 y([1999],)i(Com)n(binatorial)f(games)i(under)g(auction)g(pla)n(y) -7 b(,)30 b Fi(Games)j(Ec)l(onom.)h(Behav.)704 4541 y Fc(27)p Fj(,)27 b(229{264.)515 4649 y(523.)40 b(D.)31 b(B.)g(Leep)g(and)f(G.)h(My)n(erson)f([1999],)f(Marriage,)g(magic)h (and)g(solitaire,)g Fi(A)n(mer.)704 4749 y(Math.)h(Monthly)36 b Fc(106)p Fj(,)27 b(419{429.)515 4857 y(524.)40 b(A.)34 b(Lehman)g([1964],)e(A)j(solution)e(to)h(the)g(Shannon)g(switc)n(hing)f (game,)h Fi(SIAM)h(J.)704 4956 y(Appl.)c(Math.)e Fc(12)p Fj(,)e(687{725.)p eop %%Page: 35 35 35 34 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(35)515 523 y(525.)40 b(T.)28 b(Lengauer)e(and)i(R.)g(T)-7 b(arjan)27 b([1980],)f(The)i(space)f (complexit)n(y)h(of)g(p)r(ebble)g(games)704 623 y(on)f(trees,)g Fi(Inform.)k(Pr)l(o)l(c)l(ess.)f(L)l(ett.)e Fc(10)p Fj(,)f(184{188.)515 731 y(526.)40 b(T.)30 b(Lengauer)f(and)h(R.)g(T)-7 b(arjan)30 b([1982],)e(Asymptotically)i(tigh)n(t)h(b)r(ounds)f(on)g(time-)704 830 y(space)19 b(trade-o\013s)h(in)g(a)g(p)r(ebble)h(game,)f Fi(J.)j(Asso)l(c.)g(Comput.)h(Mach.)e Fc(29)p Fj(,)e(1087{1130.)515 938 y(527.)40 b(H.)f(W.)g(Lenstra,)f(Jr.)g([1977],)f(On)h(the)h (algebraic)e(closure)g(of)i(t)n(w)n(o,)f Fi(Pr)l(o)l(c.)j(Kon.)704 1038 y(Ne)l(derl.)31 b(A)n(kad.)f(Wetensch.)h Fj(\(Ser.)c(A\))h Fc(80)p Fj(,)g(389{396.)515 1146 y(528.)40 b(H.)27 b(W.)h(Lenstra,)e (Jr.)h([1977/1978],)c(Nim)28 b(m)n(ultiplication,)f(S)n(\023)-39 b(eminaire)26 b(de)h(Th)n(\023)-39 b(eorie)704 1245 y(des)27 b(Nom)n(bres)g(No.)g(11,)g(Univ)n(ersit)n(\023)-39 b(e)26 b(de)i(Bordeaux,)e(F)-7 b(rance.)515 1353 y(529.)40 b(D.)c(N.)h(L.)f (Levy)-7 b(,)35 b(ed.)i([1988],)d Fi(Computer)k(Games)45 b Fj(I,)36 b(I)r(I,)g(Springer-V)-7 b(erlag,)34 b(New)704 1453 y(Y)-7 b(ork,)27 b(NY.)515 1561 y(530.)40 b(J.)22 b(Lewin)h([1986],)d(The)j(lion)f(and)h(man)f(problem)g(revisited,)g Fi(J.)j(Optimization)h(The-)704 1660 y(ory)k(and)h(Applic)l(ations)36 b Fc(49)p Fj(,)27 b(411{430.)515 1768 y(531.)40 b(T.)30 b(Lewis)f(and)h(S.)g(Willard)f([1980],)g(The)g(rotating)g(table,)h Fi(Math.)j(Mag.)f Fc(53)p Fj(,)d(174{)704 1868 y(179.)515 1976 y(532.)40 b(S.-Y.)23 b(R.)h(Li)f([1974],)e(Generalized)i (impartial)f(games,)g Fi(Internat.)j(J.)h(Game)g(The)l(ory)704 2076 y Fc(3)p Fj(,)h(169{184.)515 2183 y(533.)40 b(S.-Y.)24 b(R.)g(Li)g([1976],)e(Sums)i(of)g(Zuc)n(hsw)n(ang)e(games,)h Fi(J.)k(Combin.)g(The)l(ory)36 b Fj(\(Ser.)23 b(A\))704 2283 y Fc(21)p Fj(,)k(52{67.)515 2391 y(534.)40 b(S.-Y.)29 b(R.)g(Li)g([1977],)e Fe(N)9 b Fj(-p)r(erson)28 b(nim)h(and)g Fe(N)9 b Fj(-p)r(erson)28 b(Mo)r(ore's)f(games,)h Fi(Internat.)704 2491 y(J.)i(Game)g(The)l(ory)37 b Fc(7)p Fj(,)27 b(31{36.)515 2599 y(535.)40 b(D.)29 b(Lic)n(h)n(tenstein)f([1982],)f(Planar)f(form)n (ulae)i(and)g(their)g(uses,)g Fi(SIAM)j(J.)f(Comput.)704 2698 y Fc(11)p Fj(,)d(329{343.)515 2806 y(536.)40 b(D.)g(Lic)n(h)n (tenstein)g(and)g(M.)g(Sipser)g([1980],)e(Go)h(is)h(P)n (olynomial-Space)e(hard,)h Fi(J.)704 2906 y(Asso)l(c.)27 b(Comput.)g(Mach.)f Fc(27)p Fj(,)d(393{401,)e(earlier)h(v)n(ersion)h (app)r(eared)g(in)h(Pro)r(c.)f(19th)704 3005 y(Ann.)d(Symp.)g(F)-7 b(oundations)19 b(of)g(Computer)h(Science)f(\(Ann)i(Arb)r(or,)d(MI,)i (Oct.)g(1978\),)704 3105 y(IEEE)26 b(Computer)h(So)r(c.,)h(Long)f(Beac) n(h,)f(CA,)i(1978,)e(pp.)i(48{54.)515 3213 y(537.)40 b(H.)33 b(Lieb)r(ec)n(k)g([1971],)e(Some)i(generalizations)d(of)j(the)h (14-15)c(puzzle,)k Fi(Math.)h(Mag.)704 3313 y Fc(44)p Fj(,)27 b(185{189.)515 3421 y(538.)40 b(D.)28 b(E.)f(Lo)r(eb)h([1995],) e(Ho)n(w)h(to)g(win)h(at)f(Nim,)i Fi(UMAP)h(J.)d Fc(16)p Fj(,)g(367{388.)515 3528 y(539.)40 b(D.)e(E.)f(Lo)r(eb)h([1996],)e (Stable)i(winning)f(coalitions,)g(in:)h Fi(Games)h(of)h(No)f(Chanc)l (e,)704 3628 y Fj(Pro)r(c.)21 b(MSRI)h(W)-7 b(orkshop)21 b(on)g(Com)n(binatorial)g(Games,)g(July)-7 b(,)22 b(1994,)e(Berk)n (eley)-7 b(,)21 b(CA,)704 3728 y(MSRI)i(Publ.)g(\(R.)g(J.)g(No)n(w)n (ak)n(o)n(wski,)d(ed.\),)j(V)-7 b(ol.)23 b(29,)f(Cam)n(bridge)g(Univ)n (ersit)n(y)g(Press,)704 3827 y(Cam)n(bridge,)k(pp.)i(451{471.)515 3935 y(540.)40 b(A.)23 b(M.)g(Lop)r(ez,)f(Jr.)g([1991],)f(A)i(prolog)e (Mastermind)h(program,)e Fi(J.)25 b(R)l(e)l(cr.)g(Math.)f Fc(23)p Fj(,)704 4035 y(81{93.)515 4143 y(541.)40 b(C.)23 b(M.)h(L\023)-42 b(op)r(ez)23 b([1997],)f(Chip)h(\014ring)g(and)g(the)h (T)-7 b(utte)24 b(p)r(olynomial,)f Fi(A)n(nnals)i(of)i(Com-)704 4242 y(binatorics)36 b Fc(1)p Fj(,)27 b(253{259.)515 4350 y(542.)40 b(S.)24 b(Lo)n(yd)g([1914],)e Fi(Cyclop)l(e)l(dia)30 b(of)e(Puzzles)e(and)i(T)-6 b(ricks)7 b Fj(,)25 b(F)-7 b(ranklin)24 b(Bigelo)n(w)e(Corp)r(o-)704 4450 y(ration,)28 b(Morningside)g(Press,)f(NY,)j(reissued)e(and)g(edited)i(b)n(y)e(M.)h (Gardner)f(under)704 4550 y(the)33 b(name)f Fi(The)k(Mathematic)l(al)g (Puzzles)f(of)g(Sam)f(L)l(oyd)g Fj(\(t)n(w)n(o)e(v)n(olumes\),)g(Do)n (v)n(er,)704 4649 y(New)c(Y)-7 b(ork,)27 b(NY,)h(1959.)515 4757 y(543.)40 b(X.)28 b(Lu)g([1991],)d(A)j(matc)n(hing)f(game,)g Fi(Discr)l(ete)j(Math.)f Fc(94)p Fj(,)e(199{207.)515 4865 y(544.)40 b(X.)32 b(Lu)f([1992],)f(A)h(c)n(haracterization)e(on)i Fe(n)p Fj(-critical)f(economical)g(generalized)g(tic-)704 4965 y(tac-to)r(e)d(games,)f Fi(Discr)l(ete)k(Math.)f Fc(110)p Fj(,)e(197{203.)p eop %%Page: 36 36 36 35 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(36)515 523 y(545.)40 b(X.)28 b(Lu)g([1992],)d(Hamiltonian)j(games,)e Fi(J.)k(Combin.)h(The)l(ory)39 b Fj(\(Ser.)28 b(B\))f Fc(55)p Fj(,)g(18{32.)515 631 y(546.)40 b(X.)26 b(Lu)f([1995],)e(A)j(Hamiltonian)f(game)g(on)g Fe(K)2160 643 y Fb(n;n)2265 631 y Fj(,)g Fi(Discr)l(ete)j(Math.)f Fc(142)p Fj(,)d(185{191.)515 739 y(547.)40 b(X.-M.)33 b(Lu)h([1986],)d(T)-7 b(o)n(w)n(ers)32 b(of)h(Hanoi)g(graphs,)f Fi(Intern.)i(J.)h(Comput.)h(Math.)e Fc(19)p Fj(,)704 839 y(23{38.)515 946 y(548.)40 b(X.-M.)f(Lu)h([1988],)d(T)-7 b(o)n(w)n(ers)38 b(of)h(Hanoi)g(problem)g(with)h(arbitrary)d Fe(k)45 b Ff(\025)d Fj(3)d(p)r(egs,)704 1046 y Fi(Intern.)29 b(J.)h(Comput.)g(Math.)f Fc(24)p Fj(,)f(39{54.)515 1154 y(549.)40 b(X.-M.)24 b(Lu)g([1989],)f(An)h(iterativ)n(e)f(solution)h (for)f(the)h(4-p)r(eg)g(to)n(w)n(ers)e(of)i(Hanoi,)g Fi(Com-)704 1254 y(put.)30 b(J.)d Fc(32)p Fj(,)h(187{189.)515 1362 y(550.)711 1341 y(\023)704 1362 y(E.)33 b(Lucas)g([1960],)g Fi(R)n(\023)-40 b(ecr)n(\023)g(eations)36 b(Math)n(\023)-40 b(ematiques)7 b Fj(,)35 b(V)-7 b(ol.)34 b(I)g({)f(IV,)h(A.)h(Blanc)n (hard,)704 1461 y(P)n(aris.)26 b(Previous)f(editions:)j (Gauthier-Villars,)e(P)n(aris,)g(1891{1894.)515 1569 y(551.)711 1548 y(\023)704 1569 y(E.)e(Lucas)g([1974],)f Fi(Intr)l(o)l(duction)k(aux)f(R)n(\023)-40 b(ecr)n(\023)g(eations)28 b(Math)n(\023)-40 b(ematiques:)29 b(L'A)n(rithm)n(\023)-40 b(e-)704 1669 y(tique)25 b(A)n(musante)6 b Fj(,)23 b(reprin)n(ted)f(b)n (y)h(A.)g(Blanc)n(hard,)f(P)n(aris.)f(Originally)h(published)h(b)n(y) 704 1768 y(A.)28 b(Blanc)n(hard,)e(P)n(aris,)g(1895.)515 1876 y(552.)40 b(A.)33 b(L.)g(Ludington)g([1988],)e(Length)h(of)h(the)g (7-n)n(um)n(b)r(er)f(game,)g Fi(Fib)l(onac)l(ci)k(Quart.)704 1976 y Fc(26)p Fj(,)27 b(195{204.)515 2084 y(553.)40 b(A.)47 b(Ludington-Y)-7 b(oung)47 b([1990],)e(Length)i(of)g(the)h Fe(n)p Fj(-n)n(um)n(b)r(er)e(game,)g Fi(Fib)l(onac)l(ci)704 2183 y(Quart.)27 b Fc(28)p Fj(,)g(259{265.)515 2291 y(554.)40 b(M.)26 b(Maamoun)f(and)g(H.)h(Meyniel)g([1987],)e(On)h(a)g(game)g(of)h (p)r(olicemen)f(and)h(robb)r(er,)704 2391 y Fi(Discr)l(ete)k(Appl.)h (Math.)e Fc(17)p Fj(,)e(307{309.)515 2499 y(555.)40 b(P)-7 b(.)26 b(A.)g(MacMahon)g([1921],)e Fi(New)29 b(Mathematic)l(al)h (Pastimes)7 b Fj(,)27 b(Cam)n(bridge)e(Univ)n(er-)704 2599 y(sit)n(y)i(Press,)f(Cam)n(bridge.)515 2707 y(556.)40 b(F.)26 b(Ma\013ra)n(y)f([1986],)f(On)i(k)n(ernels)f(in)h Fe(i)p Fj(-triangulated)e(graphs,)h Fi(Discr)l(ete)j(Math.)f Fc(61)p Fj(,)704 2806 y(247{251.)515 2914 y(557.)40 b(F.)k(Ma\013ra)n (y)e([1992],)h(Kernels)f(in)i(p)r(erfect)h(line-graphs,)d Fi(J.)j(Combin.)h(The)l(ory)704 3014 y Fj(\(Ser.)27 b(B\))h Fc(55)p Fj(,)f(1{8.)515 3122 y(558.)40 b(R.)e(Mans\014eld)g([1996],)f (Strategies)g(for)h(the)h(Shannon)f(switc)n(hing)f(game,)h Fi(A)n(mer.)704 3221 y(Math.)31 b(Monthly)36 b Fc(103)p Fj(,)27 b(250{252.)515 3329 y(559.)40 b(G.)g(Martin)f([1991],)e Fi(Polyomino)l(es:)44 b(Puzzles)c(and)h(Pr)l(oblems)h(in)f(Tiling)7 b Fj(,)41 b(Math.)704 3429 y(Asso)r(c.)27 b(America,)g(W)-7 b(asington,)27 b(DC.)515 3537 y(560.)40 b(J.)e(G.)h(Mauldon)f([1978],)e (Num,)j(a)f(v)-5 b(arian)n(t)38 b(of)g(nim)h(with)g(no)f(\014rst)g(pla) n(y)n(er)f(win,)704 3636 y Fi(A)n(mer.)30 b(Math.)h(Monthly)36 b Fc(85)p Fj(,)27 b(575{578.)515 3744 y(561.)40 b(D.)29 b(P)-7 b(.)29 b(McIn)n(t)n(yre)f([1942],)f(A)i(new)g(system)g(for)f (pla)n(ying)g(the)i(game)e(of)g(nim,)i Fi(A)n(mer.)704 3844 y(Math.)h(Monthly)36 b Fc(49)p Fj(,)27 b(44{46.)515 3952 y(562.)40 b(R.)29 b(McNaugh)n(ton)e([1993],)g(In\014nite)j(games)d (pla)n(y)n(ed)h(on)g(\014nite)h(graphs,)e Fi(A)n(nn.)j(Pur)l(e)704 4051 y(Appl.)h(L)l(o)l(gic)i Fc(65)p Fj(,)27 b(149{184.)515 4159 y(563.)40 b(E.)e(Mead,)g(A.)g(Rosa)f(and)h(C.)h(Huang)f([1974],)e (The)i(game)g(of)g(SIM:)g(A)h(winning)704 4259 y(strategy)26 b(for)h(the)h(second)f(pla)n(y)n(er,)f Fi(Math.)31 b(Mag.)e Fc(47)p Fj(,)f(243{247.)515 4367 y(564.)40 b(N.)e(Megiddo,)f(S.)h(L.)g (Hakimi,)f(M.)h(R.)g(Garey)-7 b(,)37 b(D.)h(S.)g(Johnson)e(and)i(C.)g (H.)g(P)n(a-)704 4467 y(padimitriou)29 b([1988],)g(The)h(complexit)n(y) f(of)h(searc)n(hing)e(a)i(graph,)e Fi(J.)k(Asso)l(c.)h(Com-)704 4566 y(put.)d(Mach.)f Fc(35)p Fj(,)e(18{44.)515 4674 y(565.)40 b(K.)23 b(Mehlhorn,)h(S.)g(N\177)-42 b(aher)24 b(and)f(M.)h(Rauc)n(h)g([1990],)e(On)i(the)g(complexit)n(y)f(of)h(a)g (game)704 4774 y(related)38 b(to)g(the)h(dictionary)e(problem,)h Fi(SIAM)h(J.)h(Comput.)f Fc(19)p Fj(,)f(902{906,)d(ear-)704 4873 y(lier)f(draft)h(app)r(eared)e(in)i(Pro)r(c.)e(30th)i(Ann.)g (Symp.)g(F)-7 b(oundations)34 b(of)g(Computer)704 4973 y(Science,)27 b(pp.)h(546{548.)p eop %%Page: 37 37 37 36 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(37)515 523 y(566.)40 b(N.)24 b(S.)g(Mendelsohn)g([1946],)e(A)i(psyc)n(hological)e(game,)h Fi(A)n(mer.)j(Math.)i(Monthly)k Fc(53)p Fj(,)704 623 y(86{88.)515 731 y(567.)40 b(C.)e(G.)h(M)n(\023)-39 b(endez)37 b([1981],)f(On)i(the)h(la)n(w)e(of)i(large)d(n)n(um)n(b)r(ers,)i (in\014nite)h(games)e(and)704 830 y(category)-7 b(,)26 b Fi(A)n(mer.)j(Math.)j(Monthly)k Fc(88)p Fj(,)27 b(40{42.)515 938 y(568.)40 b(D.)e(Mey)f([1994],)f(Finite)i(games)e(for)h(a)g (predicate)g(logic)f(without)i(con)n(tractions,)704 1038 y Fi(The)l(or)l(et.)31 b(Comput.)f(Sci.)h Fj(\(Math)d(Games\))f Fc(123)p Fj(,)g(341{349.)515 1146 y(569.)40 b(F.)26 b(Mey)n(er)f(auf)h (der)f(Heide)h([1981],)e(A)i(comparison)e(of)i(t)n(w)n(o)f(v)-5 b(ariations)24 b(of)i(a)f(p)r(ebble)704 1245 y(game)i(on)g(graphs,)f Fi(The)l(or)l(et.)31 b(Comput.)g(Sci.)d Fc(13)p Fj(,)f(315{322.)515 1353 y(570.)40 b(H.)h(Meyniel)g(and)g(J.-P)-7 b(.)41 b(Roudne\013)g([1988],)f(The)h(v)n(ertex)f(pic)n(king)g(game)h(and)f(a) 704 1453 y(v)-5 b(ariation)26 b(of)i(the)g(game)f(of)g(dots)h(and)f(b)r (o)n(xes,)g Fi(Discr)l(ete)i(Math.)h Fc(70)p Fj(,)d(311{313.)515 1561 y(571.)40 b(D.)c(Mic)n(hie)f(and)g(I.)h(Bratk)n(o)e([1987],)f (Ideas)i(on)g(kno)n(wledge)f(syn)n(thesis)h(stemming)704 1660 y(from)27 b(the)h(KBBKN)f(endgame,)g Fi(Internat.)i(Comp.)i(Chess) g(Asso)l(c.)f(J.)e Fc(10)p Fj(,)f(3{10.)515 1768 y(572.)40 b(J.)29 b(Milnor)g([1953],)f(Sums)i(of)g(p)r(ositional)f(games,)f Fi(A)n(nn.)j(of)i(Math.)g(Stud.)e Fj(\(Con)n(tri-)704 1868 y(butions)i(to)h(the)f(Theory)g(of)g(Games,)g(H.)h(W.)g(Kuhn)g (and)f(A.)h(W.)g(T)-7 b(uc)n(k)n(er,)32 b(eds.\),)704 1968 y(Princeton)26 b Fc(2)p Fj(\(28\),)i(291{301.)515 2076 y(573.)40 b(P)-7 b(.)32 b(Min)h(Lin)g([1982],)e(Principal)g (partition)i(of)f(graphs)f(and)i(connectivit)n(y)f(games,)704 2175 y Fi(J.)e(F)-6 b(r)l(anklin)30 b(Inst.)d Fc(314)p Fj(,)g(203{210.)515 2283 y(574.)40 b(S.)20 b(Minsk)n(er)f([1989],)f (The)i(to)n(w)n(ers)e(of)i(Hanoi)f(rain)n(b)r(o)n(w)f(problem:)i (coloring)e(the)i(rings,)704 2383 y Fi(J.)30 b(A)n(lgorithms)35 b Fc(10)p Fj(,)27 b(1{19.)515 2491 y(575.)40 b(S.)g(Minsk)n(er)f ([1991],)f(The)j(to)n(w)n(ers)d(of)i(An)n(t)n(w)n(erp)r(en)g(problem,)f Fi(Inform.)j(Pr)l(o)l(c)l(ess.)704 2590 y(L)l(ett.)27 b Fc(38)p Fj(,)g(107{111.)515 2698 y(576.)40 b(D.)30 b(Mo)r(ews)f([1991],)f(Sum)i(of)f(games)f(b)r(orn)i(on)f(da)n(ys)f(2)h (and)g(3,)h Fi(The)l(or)l(et.)i(Comput.)704 2798 y(Sci.)e Fj(\(Math)e(Games\))g Fc(91)p Fj(,)f(119{128.)515 2906 y(577.)40 b(D.)31 b(Mo)r(ews)f([1992],)f(P)n(ebbling)g(graphs,)g Fi(J.)k(Combin.)h(The)l(ory)41 b Fj(\(Ser.)30 b(B\))h Fc(55)p Fj(,)f(244{)704 3005 y(252.)515 3113 y(578.)40 b(D.)48 b(Mo)r(ews)g([1996],)e(Coin-sliding)h(and)g(Go,)h Fi(The)l(or)l(et.)i(Comput.)f(Sci.)g Fj(\(Math)704 3213 y(Games\))27 b Fc(164)p Fj(,)g(253{276.)515 3321 y(579.)40 b(D.)25 b(Mo)r(ews)f([1996],)f(In\014nitesimals)i(and)f(coin-sliding,)g (in:)h Fi(Games)i(of)h(No)f(Chanc)l(e,)704 3421 y Fj(Pro)r(c.)21 b(MSRI)h(W)-7 b(orkshop)21 b(on)g(Com)n(binatorial)g(Games,)g(July)-7 b(,)22 b(1994,)e(Berk)n(eley)-7 b(,)21 b(CA,)704 3520 y(MSRI)i(Publ.)g(\(R.)g(J.)g(No)n(w)n(ak)n(o)n(wski,)d(ed.\),)j(V)-7 b(ol.)23 b(29,)f(Cam)n(bridge)g(Univ)n(ersit)n(y)g(Press,)704 3620 y(Cam)n(bridge,)k(pp.)i(315{327.)515 3728 y(580.)40 b(D.)33 b(Mo)r(ews)g([1996],)e(Lo)r(op)n(y)h(games)f(and)i(Go,)g(in:)g Fi(Games)i(of)g(No)g(Chanc)l(e,)h Fj(Pro)r(c.)704 3827 y(MSRI)20 b(W)-7 b(orkshop)18 b(on)i(Com)n(binatorial)e(Games,)h(July) -7 b(,)19 b(1994,)f(Berk)n(eley)-7 b(,)19 b(CA,)h(MSRI)704 3927 y(Publ.)k(\(R.)h(J.)f(No)n(w)n(ak)n(o)n(wski,)e(ed.\),)i(V)-7 b(ol.)25 b(29,)e(Cam)n(bridge)g(Univ)n(ersit)n(y)h(Press,)f(Cam-)704 4027 y(bridge,)k(pp.)h(259{272.)515 4134 y(581.)40 b(E.)31 b(H.)i(Mo)r(ore)e([1909{1910],)d(A)k(generalization)e(of)i(the)g(game)f (called)h(nim,)h Fi(A)n(nn.)704 4234 y(of)d(Math.)h Fj(\(Ser.)d(2\))g Fc(11)p Fj(,)f(93{94.)515 4342 y(582.)40 b(F.)21 b(L.)g(Morris)e ([1981],)g(Pla)n(ying)g(disjunctiv)n(e)i(sums)f(is)h(p)r(olynomial)f (space)g(complete,)704 4442 y Fi(Internat.)29 b(J.)h(Game)g(The)l(ory) 37 b Fc(10)p Fj(,)27 b(195{205.)515 4550 y(583.)40 b(M.)30 b(Morse)e(and)i(G.)f(A.)h(Hedlund)h([1944],)d(Unending)i(c)n(hess,)e (sym)n(b)r(olic)i(dynamics)704 4649 y(and)d(a)g(problem)h(in)f (semigroups,)g Fi(Duke)i(Math.)i(J.)d Fc(11)p Fj(,)f(1{7.)515 4757 y(584.)40 b(M.)30 b(M)r(\177)-44 b(uller)29 b(and)g(R.)h(Gasser)e ([1996],)g(Exp)r(erimen)n(ts)h(in)h(computer)f(Go)g(endgames,)704 4857 y(in:)22 b Fi(Games)k(of)f(No)g(Chanc)l(e,)h Fj(Pro)r(c.)21 b(MSRI)h(W)-7 b(orkshop)21 b(on)h(Com)n(binatorial)e(Games,)p eop %%Page: 38 38 38 37 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(38)704 523 y(July)-7 b(,)34 b(1994,)e(Berk)n(eley)-7 b(,)33 b(CA,)i(MSRI)g(Publ.)f(\(R.)g(J.)h(No)n (w)n(ak)n(o)n(wski,)c(ed.\),)k(V)-7 b(ol.)34 b(29,)704 623 y(Cam)n(bridge)26 b(Univ)n(ersit)n(y)h(Press,)f(Cam)n(bridge,)g (pp.)i(273{284.)515 731 y(585.)40 b(D.)d(Mundici)g(and)g(T.)g(T)-7 b(rom)n(b)r(etta)36 b([1997],)f(Optimal)i(comparison)e(strategies)g(in) 704 830 y(Ulam's)44 b(searc)n(hing)f(game)g(with)i(t)n(w)n(o)f(errors,) e Fi(The)l(or)l(et.)47 b(Comput.)f(Sci.)g Fj(\(Math)704 930 y(Games\))27 b Fc(182)p Fj(,)g(217{232.)515 1038 y(586.)40 b(H.)c(J.)g(R.)h(Murra)n(y)d([1952],)h Fi(A)i(History)h(of)g (Bo)l(ar)l(d)h(Games)f(Other)g(Than)g(Chess)7 b Fj(,)704 1137 y(Oxford)26 b(Univ)n(ersit)n(y)h(Press.)515 1245 y(587.)40 b(B.)23 b(Nadel)g([1990],)f(Represen)n(tation)g(selection)h (for)g(constrain)n(t)f(satisfaction:)h(a)g(case)704 1345 y(study)28 b(using)f Fe(n)p Fj(-queens,)g Fi(IEEE)j(Exp)l(ert)36 b Fj(pp.)28 b(16{23.)515 1453 y(588.)40 b(A.)24 b(Napier)g([1970],)f(A) h(new)h(game)e(in)h(to)n(wn,)g(Empire)g(Mag.,)g(Den)n(v)n(er)f(P)n (ost,)g(Ma)n(y)g(2.)515 1561 y(589.)40 b(A.)f(Negro)f(and)h(M.)h (Sereno)e([1992],)g(Solution)h(of)g(Ulam's)g(problem)g(on)g(binary)704 1660 y(searc)n(h)26 b(with)i(three)f(lies,)h Fi(J.)i(Combin.)h(The)l (ory)38 b Fj(\(Ser.)28 b(A\))g Fc(59)p Fj(,)f(149{154.)515 1768 y(590.)40 b(J.)c(Ne)l(\024)-37 b(set)l(\024)g(ril)35 b(and)i(R.)g(Thomas)f([1987],)f(W)-7 b(ell)37 b(quasi)f(ordering,)f (long)i(games)e(and)704 1868 y(com)n(binatorial)28 b(study)h(of)h (undecidabilit)n(y)-7 b(,)29 b(in:)h Fi(L)l(o)l(gic)j(and)f (Combinatorics,)i(Con-)704 1968 y(temp.)29 b(Math.)f Fj(\(S.)f(G.)g(Simpson,)g(ed.\),)g(V)-7 b(ol.)27 b(65,)f(Amer.)g(Math.) h(So)r(c.,)g(Pro)n(vidence,)704 2067 y(RI,)h(pp.)g(281{293.)515 2175 y(591.)40 b(S.)28 b(Neufeld)h(and)f(R.)h(J.)e(No)n(w)n(ak)n(o)n (wski)f([1993],)g(A)i(v)n(ertex-to-v)n(ertex)e(pursuit)i(game)704 2275 y(pla)n(y)n(ed)d(with)h(disjoin)n(t)f(sets)h(of)g(edges,)f(in:)h Fi(Finite)i(and)h(In\014nite)e(Combinatorics)j(in)704 2374 y(Sets)c(and)i(L)l(o)l(gic)j Fj(\(N.)25 b(W.)h(Sauer)e(et)h(al.,)g (eds.\),)g(Klu)n(w)n(er,)e(Dordrec)n(h)n(t,)h(pp.)h(299{312.)515 2482 y(592.)40 b(S.)20 b(Neufeld)g(and)g(R.)g(J.)f(No)n(w)n(ak)n(o)n (wski)e([1998],)h(A)i(game)f(of)g(cops)g(and)h(robb)r(ers)e(pla)n(y)n (ed)704 2582 y(on)27 b(pro)r(ducts)g(of)h(graphs,)e Fi(Discr)l(ete)k (Math.)f Fc(186)p Fj(,)e(253{268.)515 2690 y(593.)40 b(R.)h(J.)f(No)n(w)n(ak)n(o)n(wski)d([1991],)i Fe(:)14 b(:)g(:)p Fj(,)41 b(W)-7 b(elter's)40 b(game,)g(Sylv)n(er)f(coinage,)g (dots-and-)704 2790 y(b)r(o)n(xes,)g Fe(:)14 b(:)g(:)p Fj(,)41 b(in:)f Fi(Combinatorial)k(Games,)f Fj(Pro)r(c.)c(Symp.)h (Appl.)h(Math.)g(\(R.)f(K.)704 2889 y(Guy)-7 b(,)28 b(ed.\),)g(V)-7 b(ol.)28 b(43,)e(Amer.)i(Math.)g(So)r(c.,)f(Pro)n(vidence,)f(RI,)i(pp.) g(155{182.)515 2997 y(594.)40 b(R.)f(J.)g(No)n(w)n(ak)n(o)n(wski)d(and) j(D.)h(G.)f(P)n(o)r(ole)f([1996],)g(Geograph)n(y)f(pla)n(y)n(ed)h(on)h (pro)r(d-)704 3097 y(ucts)33 b(of)f(directed)h(cycles,)f(in:)h Fi(Games)j(of)f(No)f(Chanc)l(e,)i Fj(Pro)r(c.)c(MSRI)h(W)-7 b(orkshop)704 3196 y(on)37 b(Com)n(binatorial)f(Games,)h(July)-7 b(,)38 b(1994,)d(Berk)n(eley)-7 b(,)37 b(CA,)h(MSRI)g(Publ.)f(\(R.)h (J.)704 3296 y(No)n(w)n(ak)n(o)n(wski,)33 b(ed.\),)j(V)-7 b(ol.)36 b(29,)f(Cam)n(bridge)f(Univ)n(ersit)n(y)h(Press,)f(Cam)n (bridge,)h(pp.)704 3396 y(329{337.)515 3504 y(595.)40 b(R.)23 b(No)n(w)n(ak)n(o)n(wski)c(and)k(P)-7 b(.)22 b(Winkler)g([1983],)f(V)-7 b(ertex-to-v)n(ertex)21 b(pursuit)h(in)h(a)f (graph,)704 3603 y Fi(Discr)l(ete)30 b(Math.)f Fc(43)p Fj(,)e(235{239.)515 3711 y(596.)40 b(S.)32 b(P)-7 b(.)32 b(Nudelman)g([1995],)f(The)h(mo)r(dular)f Fe(n)p Fj(-queens)h(problem)f (in)i(higher)e(dimen-)704 3811 y(sions,)c Fi(Discr)l(ete)i(Math.)g Fc(146)p Fj(,)e(159{167.)515 3919 y(597.)40 b(T.)22 b(H.)h(O'Beirne)e ([1984],)g Fi(Puzzles)k(and)g(Par)l(adoxes)7 b Fj(,)24 b(Do)n(v)n(er,)d(New)h(Y)-7 b(ork,)22 b(NY.)h(\(Ap-)704 4018 y(p)r(eared)k(previously)f(b)n(y)i(Oxford)e(Univ)n(ersit)n(y)h (Press,)f(London,)h(1965.\).)515 4126 y(598.)40 b(G.)35 b(L.)g(O'Brian)e([1978-79],)f(The)j(graph)e(of)i(p)r(ositions)f(in)h (the)g(game)f(of)h(SIM,)g Fi(J.)704 4226 y(R)l(e)l(cr.)29 b(Math.)g Fc(11)p Fj(,)f(3{9.)515 4334 y(599.)40 b(H.)e(K.)g(Orman)g ([1996],)e(P)n(en)n(tomino)r(es:)h(a)h(\014rst)g(pla)n(y)n(er)e(win,)j (in:)f Fi(Games)i(of)h(No)704 4433 y(Chanc)l(e,)49 b Fj(Pro)r(c.)e(MSRI)h(W)-7 b(orkshop)46 b(on)h(Com)n(binatorial)f (Games,)h(July)-7 b(,)48 b(1994,)704 4533 y(Berk)n(eley)-7 b(,)33 b(CA,)h(MSRI)h(Publ.)f(\(R.)h(J.)f(No)n(w)n(ak)n(o)n(wski,)e (ed.\),)j(V)-7 b(ol.)34 b(29,)f(Cam)n(bridge)704 4633 y(Univ)n(ersit)n(y)27 b(Press,)f(Cam)n(bridge,)g(pp.)i(339{344.)515 4741 y(600.)40 b(J.)e(P)n(ac)n(h)f([1992],)g(On)h(the)g(game)g(of)g (Misery)-7 b(,)38 b Fi(Studia)i(Sci.)g(Math.)h(Hungar.)d Fc(27)p Fj(,)704 4840 y(355{360.)p eop %%Page: 39 39 39 38 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(39)515 523 y(601.)40 b(E.)23 b(W.)h(P)n(ac)n(k)n(el)e([1987],)g(The)h(algorithm)g(designer)g(v)n (ersus)f(nature:)h(a)g(game-theore-)704 623 y(tic)28 b(approac)n(h)d(to)j(information-based)e(complexit)n(y)-7 b(,)27 b Fi(J.)j(Complexity)36 b Fc(3)p Fj(,)28 b(244{257.)515 731 y(602.)40 b(C.)21 b(H.)h(P)n(apadimitriou)d([1985],)g(Games)i (against)f(nature,)h Fi(J.)i(Comput.)i(System)e(Sci.)704 830 y Fc(31)p Fj(,)k(288{301.)515 938 y(603.)40 b(C.)31 b(H.)h(P)n(apadimitriou)e([1994],)g Fi(Computational)35 b(Complexity)7 b Fj(,)33 b(Addison-W)-7 b(esley)g(,)704 1038 y(Chapter)27 b(19:)g(P)n(olynomial)e(Space.)515 1146 y(604.)40 b(A.)g(P)n(apaioannou)c([1982],)i(A)i(Hamiltonian)f (game,)f Fi(A)n(nn.)i(Discr)l(ete)h(Math.)f Fc(13)p Fj(,)704 1245 y(171{178.)515 1353 y(605.)g(T.)35 b(D.)h(P)n(arsons)c([1978],)h (Pursuit-ev)-5 b(asion)34 b(in)h(a)g(graph,)e(in:)j Fi(The)l(ory)i(and) f(Appli-)704 1453 y(c)l(ations)h(of)h(Gr)l(aphs)45 b Fj(\(Y.)37 b(Ala)n(vi)f(and)h(D.)g(R.)g(Lic)n(k,)f(eds.\),)h (Springer-V)-7 b(erlag,)34 b(pp.)704 1553 y(426{441.)515 1660 y(606.)40 b(T.)29 b(D.)g(P)n(arsons)d([1978],)h(The)i(searc)n(h)e (n)n(um)n(b)r(er)h(of)h(a)f(connected)g(graph,)g Fi(Pr)l(o)l(c.)k(9th) 704 1760 y(South-Eastern)j(Conf.)h(on)g(Combinatorics,)h(Gr)l(aph)g (The)l(ory,)g(and)f(Computing,)p Fj(,)704 1860 y(pp.)28 b(549{554.)515 1968 y(607.)40 b(O.)20 b(P)n(atashnik)f([1980],)h (Qubic:)g(4)5 b Ff(\002)g Fj(4)g Ff(\002)g Fj(4)18 b(Tic-T)-7 b(ac-T)g(o)r(e,)19 b Fi(Math.)25 b(Mag.)d Fc(53)p Fj(,)e(202{216.)515 2076 y(608.)40 b(J.)27 b(L.)h(P)n(aul)e([1978],)g(Tic-T)-7 b(ac-T)g(o)r(e)26 b(in)i Fe(n)g Fj(dimensions,)f Fi(Math.)k(Mag.)e Fc(51)p Fj(,)f(45{49.)515 2183 y(609.)40 b(W.)e(J.)g(P)n(aul,)e(E.)i (J.)f(Prauss)f(and)i(R.)g(Reisc)n(h)n(uk)f([1980],)f(On)i(alternation,) e Fi(A)l(cta)704 2283 y(Informatic)l(a)f Fc(14)p Fj(,)27 b(243{255.)515 2391 y(610.)40 b(W.)33 b(J.)f(P)n(aul)f(and)h(R.)h (Reisc)n(h)n(uk)e([1980],)g(On)h(alternation,)f(I)r(I,)i Fi(A)l(cta)h(Informatic)l(a)704 2491 y Fc(14)p Fj(,)27 b(391{403.)515 2599 y(611.)40 b(W.)c(J.)g(P)n(aul,)f(R.)h(E.)f(T)-7 b(arjan)35 b(and)h(J.)g(R.)g(Celoni)f([1976/77],)e(Space)j(b)r(ounds)g (for)704 2698 y(a)h(game)g(on)g(graphs,)f Fi(Math.)k(Systems)e(The)l (ory)47 b Fc(10)p Fj(,)37 b(239{251,)d(correction)i(ibid.)704 2798 y Fc(11)30 b Fj(\(1977/78\),)f(85.)h(First)h(app)r(eared)f(in)h (Eigh)n(th)g(Ann)n(ual)g(A)n(CM)g(Symp)r(osium)g(on)704 2897 y(Theory)f(of)i(Computing)g(\(Hershey)-7 b(,)31 b(P)n(a.,)f(1976\),)h(Asso)r(c.)g(Comput.)h(Mac)n(h.,)f(New)704 2997 y(Y)-7 b(ork,)27 b(NY,)h(1976,)e(pp)i(149{160.)515 3105 y(612.)40 b(J.)c(P)n(earl)e([1980],)h(Asymptotic)h(prop)r(erties)g (of)g(minimax)g(trees)g(and)g(game-sear-)704 3205 y(c)n(hing)27 b(pro)r(cedures,)f Fi(A)n(rti\014cial)31 b(Intel)t(ligenc)l(e)j Fc(14)p Fj(,)28 b(113{138.)515 3313 y(613.)40 b(J.)19 b(P)n(earl)f([1984],)g Fi(Heuristics:)k(Intel)t(ligent)h(Se)l(ar)l(ch)g (Str)l(ate)l(gies)f(for)h(Computer)g(Pr)l(ob-)704 3412 y(lem)30 b(Solving)7 b Fj(,)29 b(Addison-W)-7 b(esley)g(,)27 b(Reading,)g(MA.)515 3520 y(614.)40 b(A.)26 b(P)n(ek)n(e)n(\024)-39 b(c)23 b([1996],)g(A)j(winning)g(strategy)e(for)h(the)h(Ramsey)e(graph) h(game,)f Fi(Combin.)704 3620 y(Pr)l(ob)l(ab.)31 b(Comput.)e Fc(5)p Fj(,)e(267{276.)515 3728 y(615.)40 b(A.)h(P)n(elc)f([1987],)f (Solution)h(of)h(Ulam's)f(problem)h(on)f(searc)n(hing)f(with)i(a)f (lie,)h Fi(J.)704 3827 y(Combin.)31 b(The)l(ory)39 b Fj(\(Ser.)27 b(A\))h Fc(44)p Fj(,)g(129{140.)515 3935 y(616.)40 b(A.)33 b(P)n(elc)f([1988],)g(Pre\014x)g(searc)n(h)f(with)j (a)e(lie,)h Fi(J.)i(Combin.)h(The)l(ory)44 b Fj(\(Ser.)33 b(A\))g Fc(48)p Fj(,)704 4035 y(165{173.)515 4143 y(617.)40 b(A.)d(P)n(elc)e([1989],)g(Detecting)i(errors)d(in)j(searc)n(hing)e (games,)g Fi(J.)j(Combin.)h(The)l(ory)704 4242 y Fj(\(Ser.)27 b(A\))i Fc(51)p Fj(,)e(43{54.)515 4350 y(618.)40 b(D.)35 b(H.)g(P)n(elletier)e([1987],)g(Merlin's)h(magic)f(square,)g Fi(A)n(mer.)j(Math.)i(Monthly)k Fc(94)p Fj(,)704 4450 y(143{150.)515 4558 y(619.)e(G.)32 b(L.)g(P)n(eterson)f([1979],)f (Press-Ups)h(is)h(Pspace-complete,)e(Dept.)j(of)f(Computer)704 4658 y(Science)e(The)g(Univ)n(ersit)n(y)f(of)i(Ro)r(c)n(hester)e(Ro)r (c)n(hester,)g(New)h(Y)-7 b(ork)30 b(14627,)e(unpub-)704 4757 y(lished)g(man)n(uscript.)515 4865 y(620.)40 b(G.)35 b(L.)g(P)n(eterson)e(and)i(J.)g(H.)g(Reif)h([1979],)d(Multiple-p)r (erson)i(alternation,)f Fi(Pr)l(o)l(c.)704 4965 y(20th)29 b(A)n(nn.)f(Symp.)h(F)-6 b(oundations)29 b(Computer)g(Scienc)l(e)34 b Fj(\(San)27 b(Juan,)e(Puerto)g(Rico,)p eop %%Page: 40 40 40 39 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(40)704 523 y(Oct.)27 b(1979\),)f(IEEE)h (Computer)g(So)r(c.,)g(Long)g(Beac)n(h,)g(CA,)h(pp.)g(348{363.)515 631 y(621.)40 b(N.)33 b(Pipp)r(enger)f([1980],)f(P)n(ebbling,)g Fi(Pr)l(o)l(c.)36 b(5th)f(IBM)g(Symp.)g(Math.)h(F)-6 b(oundations)704 731 y(of)30 b(Computer)h(Scienc)l(e)6 b Fj(,)28 b(IBM,)g(Japan,)e(19)h(pp.)515 839 y(622.)40 b(N.)23 b(Pipp)r(enger)e([1982],)g(Adv)-5 b(ances)22 b(in)h(p)r(ebbling,)f Fi(Pr)l(o)l(c.)k(9th)f(Internat.)g(Col)t(lo)l(q.) i(A)n(u-)704 938 y(tomata,)h(L)l(anguages)g(and)g(Pr)l(o)l(gr)l (amming,)h Fj(Lecture)c(Notes)g(in)g(Computer)g(Science)704 1038 y(\(M.)c(Nielson)f(and)g(E.)g(M.)h(Sc)n(hmidt,)g(eds.\),)g(V)-7 b(ol.)20 b(140,)f(Springer)h(V)-7 b(erlag,)19 b(New)i(Y)-7 b(ork,)704 1137 y(NY,)28 b(pp.)g(407{417.)515 1245 y(623.)40 b(T.)d(E.)f(Plam)n(b)r(ec)n(k)g([1992],)f(Daisies,)h(Ka)n(yles,)f(and)i (the)g(Sib)r(ert{Con)n(w)n(a)n(y)e(decom-)704 1345 y(p)r(osition)28 b(in)h(mis)n(\022)-39 b(ere)27 b(o)r(ctal)i(games,)e Fi(The)l(or)l(et.)32 b(Comput.)f(Sci.)h Fj(\(Math)d(Games\))f Fc(96)p Fj(,)704 1445 y(361{388.)515 1553 y(624.)40 b(V.)27 b(Pless)f([1991],)f(Games)h(and)g(co)r(des,)h(in:)g Fi(Combinatorial)k (Games,)f Fj(Pro)r(c.)c(Symp.)704 1652 y(Appl.)h(Math.)g(\(R.)g(K.)f (Guy)-7 b(,)27 b(ed.\),)g(V)-7 b(ol.)26 b(43,)g(Amer.)g(Math.)h(So)r (c.,)f(Pro)n(vidence,)f(RI,)704 1752 y(pp.)j(101{110.)515 1860 y(625.)40 b(D.)30 b(P)n(o)r(ole)f([1992],)f(The)i(b)r(ottlenec)n (k)g(to)n(w)n(ers)e(of)i(Hanoi)g(problem,)f Fi(J.)j(R)l(e)l(cr.)g (Math.)704 1959 y Fc(24)p Fj(,)27 b(203{207.)515 2067 y(626.)40 b(D.)24 b(G.)g(P)n(o)r(ole)f([1994],)f(The)h(to)n(w)n(ers)g (and)g(triangles)g(of)g(Professor)f(Claus)h(\(or,)g(P)n(ascal)704 2167 y(kno)n(ws)j(Hanoi\),)i Fi(Math.)j(Mag.)e Fc(67)p Fj(,)e(323{344.)515 2275 y(627.)40 b(J.)33 b(Propp)f([1994],)g(A)i(new) f(tak)n(e-a)n(w)n(a)n(y)d(game,)j(in:)h Fi(The)i(Lighter)g(Side)f(of)h (Mathe-)704 2374 y(matics,)g Fj(Pro)r(c.)c(E.)i(Strens)f(Memorial)g (Conf.)g(on)h(Recr.)f(Math.)g(and)h(its)g(History)-7 b(,)704 2474 y(Calgary)g(,)35 b(1986,)h(Sp)r(ectrum)i(Series)e(\(R.)i (K.)f(Guy)h(and)f(R.)h(E.)e(W)-7 b(o)r(o)r(dro)n(w,)37 b(eds.\),)704 2574 y(Math.)28 b(Asso)r(c.)f(of)g(America,)g(W)-7 b(ashington,)28 b(DC,)g(pp.)g(212{221.)515 2682 y(628.)40 b(J.)33 b(Propp)f([1996],)f(Ab)r(out)j(Da)n(vid)e(Ric)n(hman)h (\(Prologue)e(to)i(the)g(pap)r(er)g(b)n(y)g(J.)g(D.)704 2781 y(Lazarus)19 b(et)i(al.\),)f(in:)h Fi(Games)j(of)g(No)g(Chanc)l (e,)h Fj(Pro)r(c.)19 b(MSRI)i(W)-7 b(orkshop)19 b(on)i(Com)n(bi-)704 2881 y(natorial)h(Games,)i(July)-7 b(,)23 b(1994,)f(Berk)n(eley)-7 b(,)22 b(CA,)i(MSRI)h(Publ.)e(\(R.)h(J.)g(No)n(w)n(ak)n(o)n(wski,)704 2980 y(ed.\),)k(V)-7 b(ol.)28 b(29,)e(Cam)n(bridge)h(Univ)n(ersit)n(y)f (Press,)g(Cam)n(bridge,)h(p.)h(437.)515 3088 y(629.)40 b(J.)46 b(Propp)e([2000],)h(Three-pla)n(y)n(er)e(impartial)i(games,)g Fi(The)l(or)l(et.)j(Comput.)f(Sci.)704 3188 y Fj(\(Math)28 b(Games\))f Fc(233)p Fj(,)g(263{278.)515 3296 y(630.)40 b(J.)32 b(Propp)g(and)h(D.)g(Ullman)g([1992],)f(On)g(the)h(co)r(okie)f (game,)h Fi(Internat.)h(J.)g(Game)704 3396 y(The)l(ory)i Fc(20)p Fj(,)28 b(313{324.)515 3504 y(631.)40 b(P)-7 b(.)25 b(Pudl\023)-42 b(ak)25 b(and)g(J.)h(Sgall)e([1997],)g(An)i(upp)r (er)g(b)r(ound)g(for)f(a)g(comm)n(unication)g(game)704 3603 y(related)h(to)h(time-space)f(tradeo\013s,)g(in:)h Fi(The)j(Mathematics)h(of)f(Paul)f(Er)l(d})-42 b(os)35 b Fj(\(R.)27 b(L.)704 3703 y(Graham)g(and)g(J.)g(Ne)l(\024)-37 b(set)l(\024)g(ril,)26 b(eds.\),)i(V)-7 b(ol.)27 b(I,)h(Springer,)f (Berlin,)g(pp.)h(393{399.)515 3811 y(632.)40 b(A.)c(Pultr)f(and)h(F.)g (L.)f(Morris)f([1984],)g(Prohibiting)h(rep)r(etitions)h(mak)n(es)e(pla) n(ying)704 3910 y(games)26 b(substan)n(tially)h(harder,)g Fi(Internat.)i(J.)h(Game)g(The)l(ory)37 b Fc(13)p Fj(,)27 b(27{40.)515 4018 y(633.)40 b(A.)i(Pultr)f(and)h(J.)1357 3997 y(\023)1347 4018 y(Ulehla)f([1985],)f(Remarks)h(on)h(strategies)e (in)i(com)n(binatorial)704 4118 y(games,)26 b Fi(Discr)l(ete)k(Appl.)h (Math.)e Fc(12)p Fj(,)e(165{173.)515 4226 y(634.)40 b(A.)23 b(Quilliot)f([1982],)e(Discrete)j(pursuit)f(games,)f Fi(Pr)l(o)l(c.)26 b(13th)g(Conf.)g(on)f(Gr)l(aphs)h(and)704 4325 y(Combinatorics,)32 b Fj(Bo)r(ca)27 b(Raton,)g(FL.)515 4433 y(635.)40 b(A.)35 b(Quilliot)f([1985],)e(A)j(short)f(note)g(ab)r (out)g(pursuit)h(games)e(pla)n(y)n(ed)g(on)h(a)g(graph)704 4533 y(with)28 b(a)f(giv)n(en)g(gen)n(us,)g Fi(J.)i(Combin.)j(The)l (ory)38 b Fj(\(Ser.)28 b(B\))g Fc(38)p Fj(,)f(89{92.)515 4641 y(636.)40 b(M.)c(O.)f(Rabin)h([1957],)e(E\013ectiv)n(e)i (computabilit)n(y)f(of)h(winning)g(strategies,)f Fi(A)n(nn.)704 4741 y(of)c(Math.)g(Stud.)f Fj(\(Con)n(tributions)e(to)f(the)i(Theory)e (of)h(Games\),)g(Princeton)f Fc(3)p Fj(\(39\),)704 4840 y(147{157.)p eop %%Page: 41 41 41 40 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(41)515 523 y(637.)40 b(M.)29 b(O.)f(Rabin)g([1976],)f(Probabilistic)g(algorithms,)g Fi(Pr)l(o)l(c.)32 b(Symp.)f(on)g(New)f(Dir)l(e)l(c-)704 623 y(tions)d(and)g(R)l(e)l(c)l(ent)f(R)l(esults)g(in)h(A)n(lgorithms)h (and)f(Complexity)34 b Fj(\(J.)24 b(F.)h(T)-7 b(raub,)25 b(ed.\),)704 722 y(Carnegie-Mellon,)g(Academic)j(Press,)e(New)i(Y)-7 b(ork,)27 b(NY,)h(pp.)g(21{39.)515 830 y(638.)40 b(D.)29 b(Ratner)f(and)h(M.)g(W)-7 b(arm)n(uth)29 b([1990],)e(The)i(\()p Fe(n)2280 800 y Fd(2)2336 830 y Ff(\000)19 b Fj(1\)-puzzle)29 b(and)f(related)g(relo-)704 930 y(cation)f(problems,)g Fi(J.)j(Symb)l(olic)g(Comput.)f Fc(10)p Fj(,)e(111{137.)515 1038 y(639.)40 b(B.)24 b(Ra)n(vikumar)e(and)h(K.)h(B.)g(Lakshmanan)e ([1984],)g(Coping)h(with)h(kno)n(wn)g(patterns)704 1137 y(of)j(lies)h(in)g(a)f(searc)n(h)f(game,)h Fi(The)l(or)l(et.)k(Comput.) f(Sci.)f Fc(33)p Fj(,)e(85{94.)515 1245 y(640.)40 b(N.)30 b(Reading)e([1999],)g(Nim-regularit)n(y)g(of)h(graphs,)f Fi(Ele)l(ctr)l(onic)k(J.)g(Combinatorics)704 1345 y Fc(6)p Fj(,)27 b(#R11,)g(8pp.)704 1445 y(h)n(ttp://www.com)n(binatorics.org/V) -7 b(olume)p 2130 1445 25 4 v 26 w(6/v6i1to)r(c.h)n(tml)515 1553 y(641.)40 b(M.)33 b(Reic)n(hling)f([1987],)f(A)i(simpli\014ed)g (solution)f(of)h(the)g Fe(N)41 b Fj(queens')32 b(problem,)h Fi(In-)704 1652 y(form.)e(Pr)l(o)l(c)l(ess.)f(L)l(ett.)e Fc(25)p Fj(,)f(253{255.)515 1760 y(642.)40 b(J.)25 b(H.)i(Reif)f ([1984],)e(The)i(complexit)n(y)f(of)h(t)n(w)n(o-pla)n(y)n(er)d(games)i (of)h(incomplete)g(infor-)704 1860 y(mation,)e Fi(J.)i(Comput.)h (System)f(Sci.)f Fc(29)p Fj(,)f(274{301,)d(earlier)h(draft)i(en)n (titled)h(Univ)n(er-)704 1959 y(sal)32 b(games)f(of)h(incomplete)h (information,)f(app)r(eared)f(in)i(Pro)r(c.)e(11th)h(Ann.)h(A)n(CM)704 2059 y(Symp.)24 b(Theory)f(of)h(Computing)g(\(A)n(tlan)n(ta,)g(GA,)h (1979\),)d(Asso)r(c.)i(Comput.)h(Mac)n(h.,)704 2159 y(New)j(Y)-7 b(ork,)27 b(NY,)h(pp.)g(288{308.)515 2267 y(643.)40 b(S.)35 b(Reisc)n(h)g([1980],)e(Gobang)h(ist)h(PSP)-7 b(A)n(CE-v)n(ollst\177) -42 b(andig,)32 b Fi(A)l(cta)37 b(Informatic)l(a)42 b Fc(13)p Fj(,)704 2366 y(59{66.)515 2474 y(644.)e(S.)28 b(Reisc)n(h)g([1981],)e(Hex)i(ist)h(PSP)-7 b(A)n(CE-v)n(ollst\177)-42 b(andig,)25 b Fi(A)l(cta)k(Informatic)l(a)36 b Fc(15)p Fj(,)28 b(167{)704 2574 y(191.)515 2682 y(645.)40 b(M.)28 b(Ric)n(hardson)d([1953],)h(Extension)h(theorems)f(for)h(solutions)g (of)h(irre\015exiv)n(e)d(rela-)704 2781 y(tions,)i Fi(Pr)l(o)l(c.)k (Nat.)f(A)l(c)l(ad.)g(Sci.)h(USA)c Fc(39)p Fj(,)g(649.)515 2889 y(646.)40 b(M.)27 b(Ric)n(hardson)e([1953],)g(Solutions)i(of)f (irre\015exiv)n(e)f(relations,)h Fi(A)n(nn.)i(of)i(Math.)e Fc(58)p Fj(,)704 2989 y(573{590.)515 3097 y(647.)40 b(R.)g(D.)h (Ringeisen)f([1974],)f(Isolation,)g(a)h(game)f(on)h(a)g(graph,)f Fi(Math.)k(Mag.)e Fc(47)p Fj(,)704 3196 y(132{138.)515 3304 y(648.)f(R.)30 b(L.)g(Riv)n(est,)f(A.)h(R.)g(Mey)n(er,)f(D.)h(J.)g (Kleitman,)f(K.)h(Winklman)g(and)g(J.)f(Sp)r(encer)704 3404 y([1980],)21 b(Coping)i(with)h(errors)d(in)i(binary)g(searc)n(h)e (pro)r(cedures,)h Fi(J.)k(Comput.)g(System)704 3504 y(Sci.)i Fc(20)p Fj(,)g(396{404.)515 3611 y(649.)40 b(I.)20 b(Rivin,)f(I.)h(V)-7 b(ardi)19 b(and)h(P)-7 b(.)19 b(Zimmermann)g([1994],)f(The)i Fe(n)p Fj(-queens)f(problem,)g Fi(A)n(mer.)704 3711 y(Math.)31 b(Monthly)36 b Fc(101)p Fj(,)27 b(629{638.)515 3819 y(650.)40 b(I.)f(Rivin)h(and)f(R.)h(Zabih)f([1992],)f(A)i(dynamic)f(programming)e (solution)i(to)h(the)704 3919 y Fe(N)9 b Fj(-queens)27 b(problem,)g Fi(Inform.)j(Pr)l(o)l(c)l(ess.)h(L)l(ett.)c Fc(41)p Fj(,)g(253{256.)515 4027 y(651.)40 b(E.)30 b(Rob)r(ertson)h (and)g(I.)g(Munro)f([1978],)f(NP-completeness,)h(puzzles)h(and)g (games,)704 4126 y Fi(Utilitas)f(Math.)f Fc(13)p Fj(,)e(99{116.)515 4234 y(652.)40 b(A.)g(G.)h(Robinson)f(and)g(A.)g(J.)g(Goldman)g ([1989],)f(The)h(set)g(coincidence)g(game:)704 4334 y(complexit)n(y)-7 b(,)41 b(attainabilit)n(y)-7 b(,)41 b(and)g(symmetric)g(strategies,)f Fi(J.)i(Comput.)h(System)704 4433 y(Sci.)28 b Fc(39)p Fj(,)g(376{387.)515 4541 y(653.)40 b(A.)26 b(G.)f(Robinson)g(and)g(A.)h (J.)f(Goldman)g([1990],)f(On)h(Ringeisen's)g(isolation)f(game,)704 4641 y Fi(Discr)l(ete)30 b(Math.)f Fc(80)p Fj(,)e(297{312.)515 4749 y(654.)40 b(A.)30 b(G.)g(Robinson)g(and)f(A.)i(J.)f(Goldman)f ([1990],)f(On)i(the)g(set)g(coincidence)g(game,)704 4848 y Fi(Discr)l(ete)g(Math.)f Fc(84)p Fj(,)e(261{283.)p eop %%Page: 42 42 42 41 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(42)515 523 y(655.)40 b(A.)26 b(G.)f(Robinson)g(and)g(A.)h(J.)f(Goldman)g([1991],)f(On)h(Ringeisen's) g(isolation)f(game,)704 623 y(I)r(I,)k Fi(Discr)l(ete)i(Math.)f Fc(90)p Fj(,)e(153{167.)515 731 y(656.)40 b(A.)27 b(G.)g(Robinson)f (and)g(A.)h(J.)g(Goldman)f([1993],)f(The)h(isolation)g(game)g(for)g (regular)704 830 y(graphs,)g Fi(Discr)l(ete)k(Math.)f Fc(112)p Fj(,)e(173{184.)515 938 y(657.)40 b(J.)26 b(M.)i(Robson)e ([1983],)f(The)i(complexit)n(y)f(of)h(Go,)f Fi(Pr)l(o)l(c.)k (Information)g(Pr)l(o)l(c)l(essing)704 1038 y Fj(83)d(\(R.)h(E.)f(A.)h (Mason,)f(ed.\),)h(Elsevier,)e(Amsterdam,)h(pp.)h(413{417.)515 1146 y(658.)40 b(J.)18 b(M.)h(Robson)f([1984],)f(Com)n(binatorial)g (games)h(with)h(exp)r(onen)n(tial)f(space)g(complete)704 1245 y(decision)25 b(problems,)h Fi(Pr)l(o)l(c.)j(11th)g(Symp.)g(Math.) h(F)-6 b(oundations)29 b(of)g(Computer)g(Sci-)704 1345 y(enc)l(e,)36 b Fj(Praha,)c(Czec)n(hoslo)n(v)-5 b(akia,)31 b(Lecture)j(Notes)g(in)g(Computer)g(Science)g(\(M.)g(P)-7 b(.)704 1445 y(Ch)n(ytie)27 b(and)h(V.)g(Koub)r(ek,)f(eds.\),)h(V)-7 b(ol.)27 b(176,)g(Springer,)f(Berlin,)h(pp.)h(498{506.)515 1553 y(659.)40 b(J.)f(M.)h(Robson)f([1984],)f Fe(N)48 b Fj(b)n(y)40 b Fe(N)48 b Fj(c)n(hec)n(k)n(ers)38 b(is)h(Exptime)h (complete,)f Fi(SIAM)i(J.)704 1652 y(Comput.)28 b Fc(13)p Fj(,)f(252{267.)515 1760 y(660.)40 b(J.)24 b(M.)g(Robson)f([1985],)f (Alternation)h(with)i(restrictions)d(on)i(lo)r(oping,)f Fi(Inform.)k(and)704 1860 y(Contr)l(ol)37 b Fc(67)p Fj(,)27 b(2{11.)515 1968 y(661.)40 b(E.)32 b(Y.)g(Ro)r(din)h([1989],)d(A)j (pursuit-ev)-5 b(asion)31 b(bibliograph)n(y)f({)i(v)n(ersion)e(2,)i Fi(Comput.)704 2067 y(Math.)f(Appl.)e Fc(18)p Fj(,)e(245{250.)515 2175 y(662.)40 b(J.)g(S.)g(Rohl)h([1983],)d(A)j(faster)e (lexicographical)f Fe(n)p Fj(-queens)i(algorithm,)f Fi(Inform.)704 2275 y(Pr)l(o)l(c)l(ess.)30 b(L)l(ett.)e Fc(17)p Fj(,)f(231{233.)515 2383 y(663.)40 b(I.)19 b(Roizen)h(and)f(J.)g(P)n(earl)f([1983],)g(A)h (minimax)h(algorithm)e(b)r(etter)i(than)g(alpha-b)r(eta?)704 2482 y(Y)-7 b(es)28 b(and)f(no,)g Fi(A)n(rti\014cial)k(Intel)t(ligenc)l (e)j Fc(21)p Fj(,)28 b(199{220.)515 2590 y(664.)40 b(I.)30 b(Rosenholtz)f([1993],)f(Solving)h(some)g(v)-5 b(ariations)29 b(on)g(a)h(v)-5 b(arian)n(t)29 b(of)h(Tic-T)-7 b(ac-T)g(o)r(e)704 2690 y(using)27 b(in)n(v)-5 b(arian)n(t)27 b(subsets,)g Fi(J.)j(R)l(e)l(cr.)f(Math.)g Fc(25)p Fj(,)f(128{135.)515 2798 y(665.)40 b(A.)23 b(S.)g(C.)f(Ross)g([1953],)f(The)h(name)h(of)f (the)h(game)f(of)g(Nim,)h(Note)g(2334,)e Fi(Math.)26 b(Gaz.)704 2897 y Fc(37)p Fj(,)h(119{120.)515 3005 y(666.)40 b(A.)27 b(E.)e(Roth)i([1978],)d(A)j(note)f(concerning)f(asymmetric)h (games)f(on)h(graphs,)f Fi(Naval)704 3105 y(R)l(es.)k(L)l(o)l(gistics) 36 b Fc(25)p Fj(,)27 b(365{367.)515 3213 y(667.)40 b(A.)47 b(E.)f(Roth)h([1978],)e(Tw)n(o-p)r(erson)f(games)i(on)g(graphs,)g Fi(J.)h(Combin.)h(The)l(ory)704 3313 y Fj(\(Ser.)27 b(B\))h Fc(24)p Fj(,)f(238{241.)515 3421 y(668.)40 b(T.)24 b(Roth)g([1974],)e (The)i(to)n(w)n(er)f(of)h(Brahma)e(revisited,)i Fi(J.)i(R)l(e)l(cr.)g (Math.)g Fc(7)p Fj(,)d(116{119.)515 3528 y(669.)40 b(E.)28 b(M.)g(Rounds)g(and)g(S.)h(S.)f(Y)-7 b(au)28 b([1974],)f(A)h(winning)h (strategy)e(for)g(SIM,)i Fi(J.)h(R)l(e)l(cr.)704 3628 y(Math.)f Fc(7)p Fj(,)e(193{202.)515 3736 y(670.)40 b(W.)35 b(L.)g(Ruzzo)g([1980],)e(T)-7 b(ree-size)34 b(b)r(ounded)i (alternation,)e Fi(J.)i(Comput.)h(Systems)704 3836 y(Sci.)28 b Fc(21)p Fj(,)g(218{235.)515 3944 y(671.)40 b(S.)28 b(Sac)n(kson)e([1946],)g Fi(A)j(Gamut)h(of)g(Games)7 b Fj(,)28 b(Random)g(House.)515 4051 y(672.)40 b(M.)23 b(Saks)f(and)h(A.)g(Wigderson)f([1986],)f(Probabilistic)h(Bo)r(olean)f (decision)i(trees)f(and)704 4151 y(the)30 b(complexit)n(y)f(of)g(ev)-5 b(aluating)29 b(game)f(trees,)h Fi(Pr)l(o)l(c.)k(27th)f(A)n(nn.)f (Symp.)h(F)-6 b(ounda-)704 4251 y(tions)24 b(of)h(Computer)f(Scienc)l (e)31 b Fj(\(T)-7 b(oron)n(to,)20 b(On)n(t.,)h(Canada\),)f(IEEE)g (Computer)h(So)r(c.,)704 4350 y(W)-7 b(ashington,)27 b(DC,)h(pp.)g(29{38.)515 4458 y(673.)40 b(U.)25 b(K.)f(Sark)-5 b(ar)23 b([2000],)f(On)j(the)f(design)g(of)h(a)f(constructiv)n(e)f (algorithm)g(to)h(solv)n(e)g(the)704 4558 y(m)n(ulti-p)r(eg)i(to)n(w)n (ers)f(of)i(Hanoi)f(problem,)g Fi(The)l(or)l(et.)k(Comput.)g(Sci.)f Fj(\(Math)e(Games\))704 4658 y Fc(237)p Fj(,)g(407{421.)515 4765 y(674.)40 b(M.)24 b(Sato)f([1972],)f(Grundy)i(functions)g(and)g (linear)f(games,)g Fi(Publ.)k(R)l(es.)f(Inst.)g(Math.)704 4865 y(Scienc)l(es,)k Fj(Ky)n(oto)c(Univ.)i Fc(7)p Fj(,)g(645{658.)p eop %%Page: 43 43 43 42 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(43)515 523 y(675.)40 b(W.)20 b(L.)f(Sc)n(haaf)f([1955,)g(1970,)f(1973,)g(1978],)h Fi(A)k(Biblio)l(gr)l(aphy)j(of)e(R)l(e)l(cr)l(e)l(ational)f(Math-)704 623 y(ematics)7 b Fj(,)32 b(V)-7 b(ol.)31 b(I)h({)f(IV,)h(Nat'l.)f (Council)h(of)f(T)-7 b(eac)n(hers)30 b(of)h(Mathematics,)g(Reston,)704 722 y(V)-9 b(A.)515 830 y(676.)40 b(T.)23 b(J.)h(Sc)n(haefer)f([1976],) e(Complexit)n(y)i(of)h(decision)f(problems)g(based)g(on)g(\014nite)h(t) n(w)n(o-)704 930 y(p)r(erson)k(p)r(erfect)i(information)e(games,)g Fi(Pr)l(o)l(c.)k(8th)g(A)n(nn.)e(A)n(CM)i(Symp.)f(The)l(ory)i(of)704 1029 y(Computing)40 b Fj(\(Hershey)-7 b(,)31 b(P)-7 b(A,)31 b(1976\),)e(Asso)r(c.)i(Comput.)g(Mac)n(h.,)f(New)h(Y)-7 b(ork,)30 b(NY,)704 1129 y(pp.)e(41{49.)515 1237 y(677.)40 b(T.)25 b(J.)h(Sc)n(haefer)e([1978],)g(On)h(the)h(complexit)n(y)f(of)g (some)g(t)n(w)n(o-p)r(erson)f(p)r(erfect-infor-)704 1337 y(mation)j(games,)g Fi(J.)j(Comput.)g(System)f(Sci.)g Fc(16)p Fj(,)e(185{225.)515 1445 y(678.)40 b(J.)22 b(Sc)n(hae\013er)g (and)h(R.)g(Lak)n(e)f([1996],)f(Solving)h(the)h(game)f(of)g(c)n(hec)n (k)n(ers,)f(in:)i Fi(Games)j(of)704 1544 y(No)32 b(Chanc)l(e,)i Fj(Pro)r(c.)29 b(MSRI)i(W)-7 b(orkshop)29 b(on)h(Com)n(binatorial)f (Games,)h(July)-7 b(,)30 b(1994,)704 1644 y(Berk)n(eley)-7 b(,)33 b(CA,)h(MSRI)h(Publ.)f(\(R.)h(J.)f(No)n(w)n(ak)n(o)n(wski,)e (ed.\),)j(V)-7 b(ol.)34 b(29,)f(Cam)n(bridge)704 1743 y(Univ)n(ersit)n(y)27 b(Press,)f(Cam)n(bridge,)g(pp.)i(119{133.)704 1843 y(h)n(ttp://www.msri.org/publications/b)r(o)r(oks/Bo)r(ok2)o(9/)o (\014les/sc)m(hae\013er.ps)o(.gz)515 1951 y(679.)40 b(M.)25 b(Sc)n(heep)r(ers)g([1994],)e(V)-7 b(ariations)24 b(on)h(a)g(game)f(of) h(Gale)g(\(I)r(I\):)i(Mark)n(o)n(v)22 b(strategies,)704 2051 y Fi(The)l(or)l(et.)31 b(Comput.)f(Sci.)h Fj(\(Math)d(Games\))f Fc(129)p Fj(,)g(385{396.)515 2159 y(680.)40 b(G.)35 b(Sc)n(hmidt)h(and) f(T.)h(Str\177)-42 b(ohlein)35 b([1985],)e(On)i(k)n(ernels)g(of)g (graphs)f(and)h(solutions)704 2258 y(of)28 b(games:)e(a)i(synopsis)e (based)h(on)h(relations)e(and)i(\014xp)r(oin)n(ts,)f Fi(SIAM)j(J.)g(A)n(lg.)g(Disc.)704 2358 y(Math.)f Fc(6)p Fj(,)e(54{65.)515 2466 y(681.)40 b(R.)c(W.)g(Sc)n(hmittb)r(erger)f ([1992],)f Fi(New)j(R)n(ules)f(for)i(Classic)h(Games)7 b Fj(,)36 b(Wiley)-7 b(,)36 b(New)704 2565 y(Y)-7 b(ork.)515 2673 y(682.)40 b(G.)e(Sc)n(hrage)f([1985],)f(A)j(t)n(w)n(o-dimensional) d(generalization)h(of)h(Grundy's)g(game,)704 2773 y Fi(Fib)l(onac)l(ci) 31 b(Quart.)d Fc(23)p Fj(,)f(325{329.)515 2881 y(683.)40 b(H.)j(Sc)n(h)n(ub)r(ert)g([1953],)e Fi(Mathematische)46 b(Mussestunden)6 b Fj(,)43 b(De)g(Gruyter,)f(Berlin,)704 2980 y(neub)r(earb)r(eitet)28 b(v)n(on)f(F.)h(Fitting,)g(Elfte)g (Au\015age.)515 3088 y(684.)40 b(F.)26 b(Sc)n(h)n(uh)g([1952],)e(Sp)r (el)j(v)-5 b(an)25 b(delers)h(\(The)g(game)f(of)h(divisors\),)f Fi(Nieuw)j(Tijdschrift)704 3188 y(vo)l(or)i(Wiskunde)35 b Fc(39)p Fj(,)27 b(299{304.)515 3296 y(685.)40 b(F.)e(Sc)n(h)n(uh)f ([1968],)f Fi(The)k(Master)f(Bo)l(ok)i(of)e(Mathematic)l(al)i(R)l(e)l (cr)l(e)l(ations)7 b Fj(,)37 b(Do)n(v)n(er,)704 3396 y(New)28 b(Y)-7 b(ork,)27 b(NY,)h(translated)f(b)n(y)g(F.)h(G\177)-42 b(ob)r(el,)28 b(edited)g(b)n(y)f(T.)h(H.)g(O'Beirne.)515 3504 y(686.)40 b(B.)27 b(L.)h(Sc)n(h)n(w)n(artz)e([1971],)g(Some)h (extensions)g(of)h(Nim,)g Fi(Math.)j(Mag.)e Fc(44)p Fj(,)f(252{257.)515 3611 y(687.)40 b(B.)33 b(L.)h(Sc)n(h)n(w)n(artz,)d(ed.)j([1979],)e Fi(Mathematic)l(al)37 b(solitair)l(es)f(and)g(games)7 b Fj(,)34 b(Ba)n(yw)n(o)r(o)r(d)704 3711 y(Publishing)27 b(Compan)n(y)-7 b(,)27 b(F)-7 b(armingdale,)26 b(NY,)i(pp.)g(37{81.)515 3819 y(688.)40 b(A.)28 b(J.)f(Sc)n(h)n(w)n(enk)g([1970],)f(T)-7 b(ak)n(e-a)n(w)n(a)n(y)24 b(games,)j Fi(Fib)l(onac)l(ci)k(Quart.)c Fc(8)p Fj(,)h(225{234.)515 3927 y(689.)40 b(A.)27 b(J.)f(Sc)n(h)n(w)n (enk)g([2000],)f(What)i(is)g(the)g(correct)e(w)n(a)n(y)g(to)i(seed)f(a) h(kno)r(c)n(k)n(out)e(tourna-)704 4027 y(men)n(t?,)j Fi(A)n(mer.)i(Math.)h(Monthly)36 b Fc(107)p Fj(,)27 b(140{150.)515 4134 y(690.)40 b(R.)22 b(S.)h(Scorer,)e(P)-7 b(.)22 b(M.)g(Grundy)g (and)h(C.)f(A.)h(B.)f(Smith)h([1944],)e(Some)h(binary)f(games,)704 4234 y Fi(Math.)31 b(Gaz.)e Fc(28)p Fj(,)e(96{103.)515 4342 y(691.)714 4321 y(\023)704 4342 y(A.)21 b(Seress)f([1992],)g(On)h (Ha)5 b(jnal's)20 b(triangle-free)g(game,)g Fi(Gr)l(aphs)25 b(Combin.)d Fc(8)p Fj(,)f(75{79.)515 4450 y(692.)714 4429 y(\023)704 4450 y(A.)40 b(Seress)f(and)g(T.)h(Szab\023)-42 b(o)39 b([1999],)f(On)i(Erd\177)-42 b(os')38 b(Eulerian)h(trail)g (game,)g Fi(Gr)l(aphs)704 4550 y(Combin.)29 b Fc(15)p Fj(,)e(233{237.)515 4658 y(693.)40 b(L.)27 b(E.)h(Shader)f([1978],)f (Another)h(strategy)f(for)h(SIM,)h Fi(Math.)j(Mag.)e Fc(51)p Fj(,)f(60{64.)515 4765 y(694.)40 b(L.)34 b(E.)f(Shader)h(and)g (M.)g(L.)g(Co)r(ok)f([1980],)f(A)i(winning)g(strategy)f(for)g(the)i (second)704 4865 y(pla)n(y)n(er)e(in)i(the)g(game)f(Tri-tip,)g Fi(Pr)l(o)l(c.)j(T)-6 b(enth)36 b(S.E.)h(Confer)l(enc)l(e)h(on)e (Computing,)704 4965 y(Combinatorics)c(and)e(Gr)l(aph)h(The)l(ory)7 b Fj(,)30 b(Utilitas,)e(Winnip)r(eg.)p eop %%Page: 44 44 44 43 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(44)515 523 y(695.)40 b(A.)21 b(S.)f(Shaki)h([1979],)d(Algebraic)i(solutions)f(of)i(partizan)e(games) h(with)h(cycles,)f Fi(Math.)704 623 y(Pr)l(o)l(c.)30 b(Camb.)i(Phil.)f(So)l(c.)d Fc(85)p Fj(,)g(227{246.)515 731 y(696.)40 b(A.)g(Shamir,)f(R.)h(L.)g(Riv)n(est)g(and)f(L.)h(M.)g (Adleman)g([1981],)e(Men)n(tal)h(P)n(ok)n(er,)f(in:)704 830 y Fi(The)k(Mathematic)l(al)h(Gar)l(dner)50 b Fj(\(D.)41 b(A.)g(Klarner,)e(ed.\),)h(W)-7 b(adsw)n(orth)39 b(In)n(ternat.,)704 930 y(Belmon)n(t,)27 b(CA,)h(pp.)g(37{43.)515 1038 y(697.)40 b(G.)28 b(J.)g(Sherman)g([1978],)e(A)i(c)n(hild's)g(game)f(with)i(p)r (erm)n(utations,)e Fi(Math.)32 b(Mag.)d Fc(51)p Fj(,)704 1137 y(67{68.)515 1245 y(698.)40 b(W.)28 b(L.)h(Sib)r(ert)f(and)g(J.)g (H.)g(Con)n(w)n(a)n(y)f([1992],)f(Mathematical)i(Ka)n(yles,)e Fi(Internat.)k(J.)704 1345 y(Game)g(The)l(ory)37 b Fc(20)p Fj(,)27 b(237{246.)515 1453 y(699.)40 b(R.)27 b(Silb)r(er)h([1976],)d (A)j(Fib)r(onacci)f(prop)r(ert)n(y)f(of)h(Wytho\013)h(pairs,)e Fi(Fib)l(onac)l(ci)31 b(Quart.)704 1553 y Fc(14)p Fj(,)c(380{384.)515 1660 y(700.)40 b(R.)29 b(Silb)r(er)g([1977],)e(Wytho\013)6 b('s)30 b(Nim)g(and)f(Fib)r(onacci)f(represen)n(tations,)f Fi(Fib)l(onac)l(ci)704 1760 y(Quart.)g Fc(15)p Fj(,)g(85{88.)515 1868 y(701.)40 b(J.-N.)29 b(O.)h(Silv)-5 b(a)29 b([1993],)f(Some)i (game)e(b)r(ounds)i(dep)r(ending)g(on)g(birthda)n(ys,)e Fi(Portu-)704 1968 y(galiae)j(Math.)e Fc(3)p Fj(,)f(353{358.)515 2076 y(702.)40 b(R.)22 b(Silv)n(er)f([1967],)g(The)h(group)f(of)h (automorphisms)f(of)h(the)g(game)f(of)h(3-dimensional)704 2175 y(tic)n(ktac)n(kto)r(e,)27 b Fi(A)n(mer.)i(Math.)i(Monthly)37 b Fc(74)p Fj(,)27 b(247{254.)515 2283 y(703.)40 b(D.)28 b(L.)g(Silv)n(erman)e([1971],)g Fi(Y)-6 b(our)29 b(Move)6 b Fj(,)29 b(McGra)n(w-Hill.)515 2391 y(704.)40 b(G.)28 b(J.)f(Simmons)h([1969],)e(The)h(game)g(of)h(SIM,)g Fi(J.)h(R)l(e)l (cr.)h(Math.)f Fc(2)p Fj(,)e(193{202.)515 2499 y(705.)40 b(D.)25 b(Singmaster)e([1981],)g(Almost)h(all)g(games)f(are)g(\014rst)h (p)r(erson)g(games,)f Fi(Eur)l(eka)31 b Fc(41)p Fj(,)704 2599 y(33{37.)515 2707 y(706.)40 b(D.)20 b(Singmaster)e([1982],)g (Almost)h(all)g(partizan)g(games)f(are)h(\014rst)g(p)r(erson)f(and)i (almost)704 2806 y(all)27 b(impartial)g(games)f(are)h(maximal,)g Fi(J.)i(Combin.)j(Inform.)e(System)f(Sci.)g Fc(7)p Fj(,)e(270{)704 2906 y(274.)515 3014 y(707.)40 b(C.)21 b(A.)h(B.)f(Smith)h([1966],)e (Graphs)g(and)h(comp)r(osite)g(games,)g Fi(J.)j(Combin.)h(The)l(ory)30 b Fc(1)p Fj(,)704 3113 y(51{81,)22 b(reprin)n(ted)i(in)h(sligh)n(tly)f (mo)r(di\014ed)h(form)f(in:)h Fi(A)i(Seminar)g(on)g(Gr)l(aph)h(The)l (ory)704 3213 y Fj(\(F.)g(Harary)-7 b(,)26 b(ed.\),)i(Holt,)g(Rinehart) f(and)h(Winston,)g(New)f(Y)-7 b(ork,)27 b(NY,)i(1967.)515 3321 y(708.)40 b(C.)26 b(A.)h(B.)g(Smith)g([1968],)e(Comp)r(ound)i (games)e(with)i(coun)n(ters,)f Fi(J.)j(R)l(e)l(cr.)f(Math.)g Fc(1)p Fj(,)704 3421 y(67{77.)515 3528 y(709.)40 b(C.)24 b(A.)g(B.)f(Smith)i([1971],)c(Simple)k(game)d(theory)h(and)h(its)f (applications,)g Fi(Bul)t(l.)k(Inst.)704 3628 y(Math.)k(Appl.)e Fc(7)p Fj(,)e(352{357.)515 3736 y(710.)40 b(D.)34 b(E.)f(Smith)i(and)e (C.)h(C.)g(Eaton)f([1911],)e(Rithmomac)n(hia,)j(the)g(great)e(mediev)-5 b(al)704 3836 y(n)n(um)n(b)r(er)27 b(game,)g Fi(A)n(mer.)j(Math.)h (Montly)36 b Fc(18)p Fj(,)27 b(73{80.)515 3944 y(711.)40 b(R.)30 b(Sosic)e(and)i(J.)f(Gu)h([1990],)d(A)j(p)r(olynomial)f(time)h (algorithm)e(for)h(the)h Fe(n)p Fj(-queens)704 4043 y(problem,)d Fi(SIGAR)-6 b(T)38 b Fc(1)p Fj(,)27 b(7{11.)515 4151 y(712.)40 b(J.)21 b(Sp)r(encer)g([1977],)e(Balancing)h(games,)g Fi(J.)k(Combin.)h(The)l(ory)32 b Fj(\(Ser.)21 b(B\))h Fc(23)p Fj(,)e(68{74.)515 4259 y(713.)40 b(J.)27 b(Sp)r(encer)h ([1984],)e(Guess)h(a)g(n)n(um)n(b)r(er)h(with)g(lying,)f Fi(Math.)k(Mag.)e Fc(57)p Fj(,)e(105{108.)515 4367 y(714.)40 b(J.)32 b(Sp)r(encer)f([1986],)g(Balancing)f(v)n(ectors)g(in)i(the)h (max)e(norm,)h Fi(Combinatoric)l(a)40 b Fc(6)p Fj(,)704 4467 y(55{65.)515 4575 y(715.)g(J.)32 b(Sp)r(encer)h([1991],)e (Threshold)h(sp)r(ectra)g(via)h(the)g(Ehrenfeuc)n(h)n(t)f(game,)g Fi(Discr)l(ete)704 4674 y(Appl.)f(Math.)e Fc(30)p Fj(,)e(235{252.)515 4782 y(716.)40 b(J.)24 b(Sp)r(encer)g([1992],)e(Ulam's)i(searc)n(hing)e (game)h(with)h(a)g(\014xed)g(n)n(um)n(b)r(er)g(of)f(lies,)h Fi(The-)704 4882 y(or)l(et.)30 b(Comput.)g(Sci.)h Fj(\(Math)d(Games\))f Fc(95)p Fj(,)h(307{321.)p eop %%Page: 45 45 45 44 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(45)515 523 y(717.)40 b(J.)e(Sp)r(encer)h ([1994],)e(Randomization,)h(derandomization)f(and)h(an)n(tirandomiza-) 704 623 y(tion:)28 b(three)f(games,)g Fi(The)l(or)l(et.)j(Comput.)h (Sci.)f Fj(\(Math)e(Games\))g Fc(131)p Fj(,)f(415{429.)515 731 y(718.)40 b(E.)28 b(L.)h(Spitznagel,)g(Jr.)f([1967],)f(A)i(new)g (lo)r(ok)g(at)f(the)i(\014fteen)f(puzzle,)g Fi(Math.)j(Mag.)704 830 y Fc(40)p Fj(,)27 b(171{174.)515 938 y(719.)40 b(E.)30 b(L.)g(Spitznagel,)g(Jr.)g([1973],)f(Prop)r(erties)g(of)h(a)g(game)g (based)g(on)g(Euclid's)g(algo-)704 1038 y(rithm,)e Fi(Math.)j(Mag.)e Fc(46)p Fj(,)e(87{92.)515 1146 y(720.)40 b(R.)24 b(Sprague)f ([1935{36],)1522 1125 y(\177)1511 1146 y(Ub)r(er)i(mathematisc)n(he)e (Kampfspiele,)h Fi(T^)-42 b(ohoku)28 b(Math.)g(J.)704 1245 y Fc(41)p Fj(,)f(438{444.)515 1353 y(721.)40 b(R.)24 b(Sprague)e([1937],)1396 1332 y(\177)1385 1353 y(Ub)r(er)i(zw)n(ei)g (Abarten)f(v)n(on)g(Nim,)i Fi(T^)-42 b(ohoku)27 b(Math.)h(J.)c Fc(43)p Fj(,)f(351{)704 1453 y(359.)515 1561 y(722.)40 b(R.)j(Sprague)f([1947],)g(Bemerkungen)i(\177)-44 b(ub)r(er)43 b(eine)g(sp)r(ezielle)g(Ab)r(elsc)n(he)h(Grupp)r(e,)704 1660 y Fi(Math.)31 b(Z.)d Fc(51)p Fj(,)f(82{84.)515 1768 y(723.)40 b(R.)29 b(Sprague)f([1961],)f Fi(Unterhaltsame)k(Mathematik)9 b Fj(,)30 b(View)n(eg)f(and)f(Sohn,)h(Braun-)704 1868 y(sc)n(h)n(w)n(eig,)d(P)n(ap)r(erbac)n(k)g(reprin)n(t,)h(translation)g (b)n(y)h(T.)g(H.)g(O'Beirne:)f Fi(R)l(e)l(cr)l(e)l(ations)j(in)704 1968 y(Mathematics)p Fj(,)f(Blac)n(kie,)e(1963.)515 2076 y(724.)40 b(H.)30 b(Steinhaus)g([1960],)e(De\014nitions)i(for)f(a)g (theory)g(of)h(games)f(and)g(pursuit,)h Fi(Naval)704 2175 y(R)l(es.)f(L)l(o)l(gistics)36 b Fc(7)p Fj(,)27 b(105{108.)515 2283 y(725.)40 b(V.)28 b(N.)g(Stepanenk)n(o)f([1975],)g (Grundy)g(games)g(under)h(conditions)f(of)h(semide\014nite-)704 2383 y(ness,)f Fi(Cyb)l(ernetics)35 b Fc(11)p Fj(,)28 b(167{172)c(\(trans.)j(of)h Fi(Kib)l(ernetika)g Fc(11)g Fj(\(1975\))e(145{149\).)515 2491 y(726.)40 b(B.)27 b(M.)g(Stew)n(art)g ([1939],)e(Problem)h(3918)f(\()p Fe(k)s Fj(-p)r(eg)i(to)n(w)n(er)f(of)h (Hanoi\),)g Fi(A)n(mer.)j(Math.)704 2590 y(Monthly)35 b Fc(46)p Fj(,)26 b(363,)g(solution)g(b)n(y)g(J.)h(S.)f(F)-7 b(rame,)27 b Fi(ibid.)h Fc(48)f Fj(\(1941\))e(216{217;)e(b)n(y)k(the) 704 2690 y(prop)r(oser,)f Fi(ibid.)k Fj(217{219.)515 2798 y(727.)40 b(L.)25 b(Stiller)h([1988],)e(Massiv)n(ely)g(parallel)h (retrograde)e(analysis,)h(T)-7 b(ec)n(h.)25 b(Rep.)h(BU-CS)704 2897 y(TR88{014,)f(Comp.)i(Sci.)h(Dept.,)h(Boston)d(Univ)n(ersit)n(y)-7 b(.)515 3005 y(728.)40 b(L.)d(Stiller)h([1989],)d(P)n(arallel)h (analysis)g(of)h(certain)g(endgames,)f Fi(Internat.)i(Comp.)704 3105 y(Chess)30 b(Asso)l(c.)h(J.)c Fc(12)p Fj(,)h(55{64.)515 3213 y(729.)40 b(L.)25 b(Stiller)h([1991],)d(Group)i(graphs)f(and)h (computational)g(symmetry)f(on)h(massiv)n(ely)704 3313 y(parallel)h(arc)n(hitecture,)h Fi(J.)i(Sup)l(er)l(c)l(omputing)35 b Fc(5)p Fj(,)27 b(99{117.)515 3421 y(730.)40 b(L.)e(Stiller)g([1996],) f(Multilinear)h(algebra)e(and)i(c)n(hess)f(endgames,)h(in:)g Fi(Games)i(of)704 3520 y(No)32 b(Chanc)l(e,)i Fj(Pro)r(c.)29 b(MSRI)i(W)-7 b(orkshop)29 b(on)h(Com)n(binatorial)f(Games,)h(July)-7 b(,)30 b(1994,)704 3620 y(Berk)n(eley)-7 b(,)33 b(CA,)h(MSRI)h(Publ.)f (\(R.)h(J.)f(No)n(w)n(ak)n(o)n(wski,)e(ed.\),)j(V)-7 b(ol.)34 b(29,)f(Cam)n(bridge)704 3719 y(Univ)n(ersit)n(y)27 b(Press,)f(Cam)n(bridge,)g(pp.)i(151{192.)515 3827 y(731.)40 b(D.)27 b(L.)g(Sto)r(c)n(k)g([1989],)e(Merlin's)i(magic)f(square)g (revisited,)g Fi(A)n(mer.)j(Math.)i(Monthly)704 3927 y Fc(96)p Fj(,)c(608{610.)515 4035 y(732.)40 b(L.)26 b(J.)f(Sto)r(c)n(kmey)n(er)g(and)g(A.)i(K.)e(Chandra)g([1979],)f(Pro)n (v)-5 b(ably)24 b(di\016cult)i(com)n(binato-)704 4134 y(rial)h(games,)f Fi(SIAM)k(J.)g(Comput.)e Fc(8)p Fj(,)f(151{174.)515 4242 y(733.)40 b(J.)33 b(A.)h(Storer)e([1983],)f(On)i(the)h(complexit)n (y)e(of)i(c)n(hess,)e Fi(J.)j(Comput.)h(System)e(Sci.)704 4342 y Fc(27)p Fj(,)27 b(77{100.)515 4450 y(734.)40 b(W.)28 b(E.)f(Story)g([1879],)f(Note)i(on)f(the)h("15")e(puzzle,)h Fi(A)n(mer.)j(J.)g(Math.)f Fc(2)p Fj(,)e(399{404.)515 4558 y(735.)40 b(P)-7 b(.)38 b(D.)i(Stra\016n,)e(Jr.)g([1985],)f (Three-p)r(erson)h(winner-tak)n(e-all)e(games)i(with)h(Mc-)704 4658 y(Carth)n(y's)26 b(rev)n(enge)g(rule,)i Fi(Col)t(le)l(ge)j(J.)f (Math.)f Fc(16)p Fj(,)e(386{394.)515 4765 y(736.)40 b(T.)e(Str\177)-42 b(ohlein)39 b(and)f(L.)h(Zagler)e([1977],)g(Analyzing)h(games)f(b)n(y)h (Bo)r(olean)g(matrix)704 4865 y(iteration,)27 b Fi(Discr)l(ete)j(Math.) f Fc(19)p Fj(,)e(183{193.)p eop %%Page: 46 46 46 45 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(46)515 523 y(737.)40 b(W.)30 b(Stromquist)f(and)h(D.)g(Ullman)g([1993],)e(Sequen)n(tial)h(comp)r (ounds)h(of)f(com)n(bina-)704 623 y(torial)d(games,)h Fi(The)l(or)l(et.)k(Comput.)f(Sci.)h Fj(\(Math)d(Games\))f Fc(119)p Fj(,)g(311{321.)515 731 y(738.)40 b(K.)23 b(Sugihara)f(and)h (I.)g(Suzuki)g([1989],)f(Optimal)h(algorithms)f(for)g(a)h(pursuit-ev)-5 b(asion)704 830 y(problem)27 b(in)h(grids,)e Fi(SIAM)k(J.)g(Disc.)g (Math.)f Fc(1)p Fj(,)f(126{143.)515 938 y(739.)40 b(K.)27 b(Sutner)h([1988],)e(On)h Fe(\033)s Fj(-automata,)g Fi(Complex)k (Systems)j Fc(2)p Fj(,)27 b(1{28.)515 1046 y(740.)40 b(K.)23 b(Sutner)g([1989],)f(Linear)g(cellular)h(automata)f(and)h(the)h (Garden-of-Eden,)e Fi(Math.)704 1146 y(Intel)t(ligenc)l(er)37 b Fc(11)p Fj(,)27 b(49{53.)515 1254 y(741.)40 b(K.)19 b(Sutner)h([1990],)e(The)i Fe(\033)s Fj(-game)f(and)g(cellular)g (automata,)g Fi(A)n(mer.)j(Math.)i(Monthly)704 1353 y Fc(97)p Fj(,)j(24{34.)515 1461 y(742.)40 b(K.)34 b(Sutner)g([1995],)e (On)i(the)g(computational)f(complexit)n(y)h(of)g(\014nite)g(cellular)g (au-)704 1561 y(tomata,)27 b Fi(J.)j(Comput.)g(System)f(Sci.)g Fc(50)p Fj(,)e(87{97.)515 1669 y(743.)40 b(J.)18 b(L.)h(Szw)n (arc\014ter)e(and)h(G.)h(Chat)n(y)f([1994],)e(En)n(umerating)i(the)g(k) n(ernels)g(of)g(a)g(directed)704 1768 y(graph)26 b(with)i(no)g(o)r(dd)f (circuits,)h Fi(Inform.)i(Pr)l(o)l(c)l(ess.)h(L)l(ett.)c Fc(51)p Fj(,)g(149{153.)515 1876 y(744.)40 b(A.)21 b(T)-7 b(ak)i(ahashi,)20 b(S.)h(Ueno)f(and)h(Y.)g(Ka)5 b(jitani)20 b([1995],)f(Mixed)i(searc)n(hing)e(and)h(prop)r(er-)704 1976 y(path-width,)28 b Fi(The)l(or)l(et.)j(Comput.)f(Sci.)h Fj(\(Math)d(Games\))f Fc(137)p Fj(,)g(253{268.)515 2084 y(745.)40 b(G.)20 b(T)-7 b(ardos)17 b([1988],)h(P)n(olynomial)g(b)r (ound)h(for)g(a)g(c)n(hip)h(\014ring)e(game)h(on)g(graphs,)f Fi(SIAM)704 2183 y(J.)30 b(Disc.)g(Math.)f Fc(1)p Fj(,)f(397{398.)515 2291 y(746.)40 b(M.)34 b(T)-7 b(arsi)32 b([1983],)g(Optimal)h(searc)n (h)f(on)h(some)g(game)g(trees,)g Fi(J.)i(Asso)l(c.)g(Comput.)704 2391 y(Mach.)29 b Fc(30)p Fj(,)f(389{396.)515 2499 y(747.)40 b(R.)e(T)-7 b(elg\023)-42 b(arsky)36 b([1987],)h(T)-7 b(op)r(ological)36 b(games:)h(on)h(the)g(50th)g(anniv)n(ersary)e(of)i (the)704 2599 y(Banac)n(h-Mazur)25 b(game,)i Fi(R)l(o)l(cky)j(Mountain) g(J.)f(Math.)g Fc(17)p Fj(,)f(227{276.)515 2707 y(748.)40 b(W.)31 b(F.)h(D.)g(Theron)e(and)h(G.)g(Geldenh)n(uys)g([1998],)f (Domination)h(b)n(y)g(queens)g(on)f(a)704 2806 y(square)c(b)r(eehiv)n (e,)i Fi(Discr)l(ete)h(Math.)g Fc(178)p Fj(,)e(213{220.)515 2914 y(749.)40 b(K.)33 b(Thompson)g([1986],)f(Retrograde)g(analysis)g (of)i(certain)f(endgames,)f Fi(Internat.)704 3014 y(Comp.)f(Chess)g (Asso)l(c.)f(J.)e Fc(9)p Fj(,)f(131{139.)515 3122 y(750.)40 b(H.)22 b(T)-7 b(oh)n(y)n(ama)19 b(and)j(A.)g(Adac)n(hi)f([2000],)e (Complexit)n(y)i(of)h(path)f(disco)n(v)n(ery)f(problems,)704 3221 y Fi(The)l(or)l(et.)31 b(Comput.)f(Sci.)h Fj(\(Math)d(Games\))f Fc(237)p Fj(,)g(381{406.)515 3329 y(751.)40 b(I.)31 b(T)-7 b(omescu)30 b([1990],)f(Almost)i(all)f(digraphs)g(ha)n(v)n(e)f(a)i(k)n (ernel,)f Fi(Discr)l(ete)i(Math.)g Fc(84)p Fj(,)704 3429 y(181{192.)515 3537 y(752.)40 b(R.)29 b(T)-7 b(o)l(\024)-37 b(si)n(\023)e(c)26 b(and)j(S.)1297 3516 y(\024)1295 3537 y(S)n(\023)-39 b(ceki)n(\023)g(c)26 b([1983],)i(An)h(analysis)f(of)h (some)f(partizan)g(graph)g(games,)704 3636 y Fi(Pr)l(o)l(c.)i(4th)h(Y) -6 b(ugoslav)30 b(Seminar)g(on)f(Gr)l(aph)i(The)l(ory,)h Fj(No)n(vi)27 b(Sad,)h(pp.)g(311{319.)515 3744 y(753.)40 b(A.)27 b(M.)g(T)-7 b(uring,)26 b(M.)h(A.)g(Bates,)f(B.)g(V.)i(Bo)n (wden)d(and)i(C.)g(Strac)n(hey)e([1953],)g(Digital)704 3844 y(computers)20 b(applied)h(to)g(games,)e(in:)j Fi(F)-6 b(aster)23 b(Than)h(Thought)30 b Fj(\(B.)21 b(V.)g(Bo)n(wden,)g(ed.\),) 704 3944 y(Pitman,)27 b(London,)g(pp.)h(286{310.)515 4051 y(754.)40 b(R.)31 b(Uehara)e(and)h(S.)h(Iw)n(ata)f([1990],)e (Generalized)i(Hi-Q)g(is)h(NP-complete,)f Fi(T)-6 b(r)l(ans.)704 4151 y(IEICE)39 b Fc(E73)p Fj(,)26 b(270{273.)515 4259 y(755.)40 b(J.)806 4238 y(\023)795 4259 y(Ulehla)26 b([1980],)e(A)i (complete)f(analysis)f(of)i(v)n(on)f(Neumann's)g(Hac)n(k)n(endot,)g Fi(Inter-)704 4359 y(nat.)30 b(J.)f(Game)i(The)l(ory)36 b Fc(9)p Fj(,)28 b(107{113.)515 4467 y(756.)40 b(D.)30 b(Ullman)g([1992],)e(More)g(on)i(the)g(four-n)n(um)n(b)r(ers)e(game,)h Fi(Math.)k(Mag.)e Fc(65)p Fj(,)e(170{)704 4566 y(174.)515 4674 y(757.)40 b(S.)30 b(V)-7 b(a)5 b(jda)30 b([1992],)e Fi(Mathematic)l(al)34 b(Games)f(and)f(How)h(to)f(Play)h(Them)6 b Fj(,)31 b(Ellis)f(Hor-)704 4774 y(w)n(o)r(o)r(d)d(Series)g(in)h (Mathematics)f(and)g(its)h(Applications,)g(Chic)n(hester,)f(England.) 515 4882 y(758.)40 b(H.)33 b(J.)g(v)-5 b(an)33 b(den)g(Herik)g(and)g (I.)g(S.)g(Hersc)n(h)n(b)r(erg)f([1985],)f(The)i(construction)f(of)h (an)704 4981 y(omniscien)n(t)27 b(endgame)g(database,)f Fi(Internat.)k(Comp.)h(Chess)g(Asso)l(c.)f(J.)e Fc(8)p Fj(,)f(66{87.)p eop %%Page: 47 47 47 46 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(47)515 523 y(759.)40 b(J.)30 b(v)-5 b(an)30 b(Leeu)n(w)n(en)g([1976],)e(Ha)n(ving)h(a)h(Grundy-n)n (um)n(b)r(ering)f(is)i(NP-complete,)e(Re-)704 623 y(p)r(ort)20 b(No.)g(207,)f(Computer)h(Science)g(Dept.,)h(P)n(ennsylv)-5 b(ania)19 b(State)h(Univ)n(ersit)n(y)-7 b(,)20 b(Uni-)704 722 y(v)n(ersit)n(y)26 b(P)n(ark,)g(P)-7 b(A.)515 830 y(760.)40 b(A.)32 b(J.)f(v)-5 b(an)31 b(Zan)n(ten)g([1990],)e(The)j (complexit)n(y)e(of)i(an)f(optimal)g(algorithm)f(for)h(the)704 930 y(generalized)26 b(to)n(w)n(er)g(of)i(Hanoi)f(problem,)g Fi(Intern.)i(J.)h(Comput.)h(Math.)e Fc(36)p Fj(,)e(1{8.)515 1038 y(761.)40 b(A.)24 b(J.)f(v)-5 b(an)23 b(Zan)n(ten)g([1991],)f(An)i (iterativ)n(e)e(optimal)i(algorithm)e(for)h(the)g(generalized)704 1137 y(to)n(w)n(er)j(of)i(Hanoi)f(problem,)g Fi(Intern.)i(J.)h(Comput.) g(Math.)f Fc(39)p Fj(,)f(163{168.)515 1245 y(762.)40 b(I.)25 b(V)-7 b(ardi)24 b([1990],)f Fi(Computational)28 b(R)l(e)l(cr)l(e)l(ations)f(in)g(Mathematic)l(a)6 b Fj(,)27 b(Addison)d(W)-7 b(es-)704 1345 y(ley)g(.)515 1453 y(763.)40 b(I.)c(P)-7 b(.)35 b(V)-7 b(arv)i(ak)35 b([1968],)f(Games)i(on)f(the)i (sum)f(of)g(graphs,)e Fi(Cyb)l(ernetics)44 b Fc(4)p Fj(,)35 b(49{51)704 1553 y(\(trans.)27 b(of)h Fi(Kib)l(ernetika)g Fc(4)g Fj(\(1968\))e(63{66\).)515 1660 y(764.)40 b(J.)35 b(V)-7 b(eerasam)n(y)34 b(and)i(I.)g(P)n(age)e([1994],)g(On)h(the)h(to) n(w)n(ers)e(of)i(Hanoi)f(problem)h(with)704 1760 y(m)n(ultiple)28 b(spare)e(p)r(egs,)i Fi(Intern.)h(J.)h(Comput.)g(Math.)f Fc(52)p Fj(,)f(17{22.)515 1868 y(765.)40 b(H.)26 b(V)-7 b(enk)i(atesw)n(aran)24 b(and)i(M.)g(T)-7 b(ompa)25 b([1989],)g(A)h (new)g(p)r(ebble)g(game)f(that)h(c)n(harac-)704 1968 y(terizes)h(parallel)f(complexit)n(y)h(classes,)g Fi(SIAM)i(J.)h (Comput.)e Fc(18)p Fj(,)g(533{549.)515 2076 y(766.)40 b(D.)50 b(Viaud)h([1987],)d(Une)i(strat)n(\023)-39 b(egie)48 b(g)n(\023)-39 b(en)n(\023)g(erale)47 b(p)r(our)i(jouer)h(au)g (Master-Mind,)704 2175 y Fi(RAIR)n(O)28 b(R)l(e)l(cher)l(che)i(op)n (\023)-40 b(er)l(ationel)t(le/Op)l(er)l(ations)33 b(R)l(ese)l(ar)l(ch)h Fc(21)p Fj(,)28 b(87{100.)515 2283 y(767.)40 b(J.)33 b(v)n(on)f(Neumann)h([1928],)e(Zur)i(Theorie)f(der)g(Gesellsc)n (haftsspiele,)h Fi(Math.)j(A)n(nn.)704 2383 y Fc(100)p Fj(,)27 b(295{320.)515 2491 y(768.)40 b(J.)32 b(v)n(on)f(Neumann)h(and) f(O.)h(Morgenstern)e([1953],)g Fi(The)l(ory)36 b(of)e(Games)g(and)h(Ec) l(o-)704 2590 y(nomic)30 b(Behaviour)9 b Fj(,)30 b(Princeton)d(Univ)n (ersit)n(y)f(Press,)g(Princeton,)h(NJ.,)h(3rd)f(edn.)515 2698 y(769.)40 b(J.)32 b(L.)h(W)-7 b(alsh)33 b([1953],)d(The)j(name)g (of)f(the)h(game)f(of)h(Nim,)g(Letter)f(to)h(the)g(Editor,)704 2798 y Fi(Math.)e(Gaz.)e Fc(37)p Fj(,)e(290.)515 2906 y(770.)40 b(T.)35 b(R.)h(W)-7 b(alsh)35 b([1982],)e(The)i(to)n(w)n(ers) f(of)h(Hanoi)g(revisited:)f(mo)n(ving)h(the)g(rings)f(b)n(y)704 3005 y(coun)n(ting)27 b(the)h(mo)n(v)n(es,)e Fi(Inform.)31 b(Pr)l(o)l(c)l(ess.)f(L)l(ett.)e Fc(15)p Fj(,)f(64{67.)515 3113 y(771.)40 b(T.)34 b(R.)h(W)-7 b(alsh)34 b([1983],)e(Iteration)i (strik)n(es)f(bac)n(k)g(at)h(the)h(cyclic)f(to)n(w)n(ers)e(of)i(Hanoi,) 704 3213 y Fi(Inform.)c(Pr)l(o)l(c)l(ess.)h(L)l(ett.)c Fc(16)p Fj(,)g(91{93.)515 3321 y(772.)40 b(I.)f(M.)g(W)-7 b(anless)39 b([1997],)e(On)i(the)h(p)r(erio)r(dicit)n(y)f(of)g(graph)f (games,)g Fi(A)n(ustr)l(alas.)i(J.)704 3421 y(Combin.)29 b Fc(16)p Fj(,)e(113{123.)515 3528 y(773.)40 b(R.)32 b(H.)g(W)-7 b(arren)31 b([1996],)f(Disks)i(on)f(a)h(c)n(hessb)r(oard,)e Fi(A)n(mer.)j(Math.)i(Monthly)41 b Fc(103)p Fj(,)704 3628 y(305{307.)515 3736 y(774.)f(A.)27 b(W)-7 b(ash)n(burn)27 b([1990],)f(Deterministic)h(graphical)f(games,)g Fi(J.)j(Math.)i(A)n (nal.)f(Appl.)704 3836 y Fc(153)p Fj(,)d(84{96.)515 3944 y(775.)40 b(W.)22 b(A.)h(W)-7 b(ebb)23 b([1982],)d(The)i(length)g(of)g (the)h(four-n)n(um)n(b)r(er)e(game,)g Fi(Fib)l(onac)l(ci)26 b(Quart.)704 4043 y Fc(20)p Fj(,)h(33{35.)515 4151 y(776.)40 b(C.)32 b(P)-7 b(.)31 b(W)-7 b(elter)32 b([1952],)e(The)i(adv)-5 b(ancing)31 b(op)r(eration)g(in)h(a)f(sp)r(ecial)h(ab)r(elian)f(group,) 704 4251 y Fi(Ne)l(derl.)g(A)n(kad.)f(Wetensch.)h(Pr)l(o)l(c.)f Fj(\(Ser.)e(A\))i Fc(55)f Fi(=)h(Indag.)g(Math.)p Fc(14)p Fj(,)f(304-314.)515 4359 y(777.)40 b(C.)i(P)-7 b(.)42 b(W)-7 b(elter)42 b([1954],)f(The)h(theory)f(of)i(a)e(class)h(of)g (games)f(on)h(a)f(sequence)h(of)704 4458 y(squares,)33 b(in)i(terms)f(of)h(the)g(adv)-5 b(ancing)34 b(op)r(eration)g(in)h(a)f (sp)r(ecial)g(group,)g Fi(Ne)l(derl.)704 4558 y(A)n(kad.)d(Wetensch.)f (Pr)l(o)l(c.)h Fj(\(Ser.)c(A\))j Fc(57)g Fi(=)f(Indag.)i(Math.)p Fc(16)p Fj(,)d(194-200.)515 4666 y(778.)40 b(J.)j(W)-7 b(est)44 b([1996],)d(Champion-lev)n(el)h(pla)n(y)h(of)g(domineering,)f (in:)i Fi(Games)h(of)g(No)704 4765 y(Chanc)l(e,)k Fj(Pro)r(c.)e(MSRI)h (W)-7 b(orkshop)46 b(on)h(Com)n(binatorial)f(Games,)h(July)-7 b(,)48 b(1994,)704 4865 y(Berk)n(eley)-7 b(,)33 b(CA,)h(MSRI)h(Publ.)f (\(R.)h(J.)f(No)n(w)n(ak)n(o)n(wski,)e(ed.\),)j(V)-7 b(ol.)34 b(29,)f(Cam)n(bridge)704 4965 y(Univ)n(ersit)n(y)27 b(Press,)f(Cam)n(bridge,)g(pp.)i(85{91.)p eop %%Page: 48 48 48 47 bop 515 232 a Fg(the)31 b(electr)n(onic)h(journal)f(of)g(combina) -6 b(torics)32 b(#DS2)750 b Fj(48)515 523 y(779.)40 b(J.)33 b(W)-7 b(est)33 b([1996],)f(Champion-lev)n(el)g(pla)n(y)g(of)h (dots-and-b)r(o)n(xes,)e(in:)j Fi(Games)h(of)h(No)704 623 y(Chanc)l(e,)49 b Fj(Pro)r(c.)e(MSRI)h(W)-7 b(orkshop)46 b(on)h(Com)n(binatorial)f(Games,)h(July)-7 b(,)48 b(1994,)704 722 y(Berk)n(eley)-7 b(,)33 b(CA,)h(MSRI)h(Publ.)f(\(R.)h(J.)f(No)n(w)n (ak)n(o)n(wski,)e(ed.\),)j(V)-7 b(ol.)34 b(29,)f(Cam)n(bridge)704 822 y(Univ)n(ersit)n(y)27 b(Press,)f(Cam)n(bridge,)g(pp.)i(79{84.)515 930 y(780.)40 b(J.)h(W)-7 b(est)42 b([1996],)d(New)j(v)-5 b(alues)41 b(for)g(T)-7 b(op)41 b(En)n(tails,)f(in:)i Fi(Games)h(of)g(No)f(Chanc)l(e,)704 1029 y Fj(Pro)r(c.)21 b(MSRI)h(W)-7 b(orkshop)21 b(on)g(Com)n(binatorial)g(Games,)g(July)-7 b(,)22 b(1994,)e(Berk)n(eley)-7 b(,)21 b(CA,)704 1129 y(MSRI)i(Publ.)g(\(R.)g(J.)g(No)n(w)n(ak)n(o)n(wski,)d(ed.\),)j(V)-7 b(ol.)23 b(29,)f(Cam)n(bridge)g(Univ)n(ersit)n(y)g(Press,)704 1229 y(Cam)n(bridge,)k(pp.)i(345{350.)515 1337 y(781.)40 b(M.)28 b(J.)f(Whinihan)h([1963],)e(Fib)r(onacci)h(Nim,)i Fi(Fib)l(onac)l(ci)i(Quart.)d Fc(1)p Fj(\(4\),)f(9{12.)515 1445 y(782.)40 b(R.)21 b(Wilb)r(er)g([1988],)e(White)i(p)r(ebbles)g (help,)g Fi(J.)j(Comput.)g(System)f(Sci.)e Fc(36)p Fj(,)f(108{124.)515 1553 y(783.)40 b(R.)26 b(M.)f(Wilson)g([1974],)f(Graph)h(puzzles,)g (homotop)n(y)g(and)g(the)h(alternating)e(group,)704 1652 y Fi(J.)30 b(Combin.)h(The)l(ory)38 b Fj(\(Ser.)28 b(B\))g Fc(16)p Fj(,)f(86{96.)515 1760 y(784.)40 b(D.)45 b(W)-7 b(olfe)44 b([1993],)f(Snak)n(es)g(in)i(domineering)e(games,)g Fi(The)l(or)l(et.)j(Comput.)g(Sci.)704 1860 y Fj(\(Math)28 b(Games\))f Fc(119)p Fj(,)g(323{329.)515 1968 y(785.)40 b(D.)28 b(W)-7 b(olfe)28 b([1996],)f(The)h(gamesman's)e(to)r(olkit,)i (in:)g Fi(Games)j(of)g(No)f(Chanc)l(e,)h Fj(Pro)r(c.)704 2067 y(MSRI)20 b(W)-7 b(orkshop)18 b(on)i(Com)n(binatorial)e(Games,)h (July)-7 b(,)19 b(1994,)f(Berk)n(eley)-7 b(,)19 b(CA,)h(MSRI)704 2167 y(Publ.)k(\(R.)h(J.)f(No)n(w)n(ak)n(o)n(wski,)e(ed.\),)i(V)-7 b(ol.)25 b(29,)e(Cam)n(bridge)g(Univ)n(ersit)n(y)h(Press,)f(Cam-)704 2267 y(bridge,)k(pp.)h(93{98.)515 2374 y(786.)40 b(D.)22 b(W)-7 b(o)r(o)r(d)21 b([1981],)f(The)h(to)n(w)n(ers)f(of)h(Brahma)f (and)h(Hanoi)g(revisited,)g Fi(J.)j(R)l(e)l(cr.)g(Math.)704 2474 y Fc(14)p Fj(,)j(17{24.)515 2582 y(787.)40 b(D.)29 b(W)-7 b(o)r(o)r(d)28 b([1983],)f(Adjudicating)i(a)f(to)n(w)n(ers)f(of) h(Hanoi)g(con)n(test,)g Fi(Intern.)i(J.)h(Com-)704 2682 y(put.)f(Math.)f Fc(14)p Fj(,)e(199{207.)515 2790 y(788.)40 b(J.-S.)22 b(W)-7 b(u)23 b(and)g(R.-J.)f(Chen)h([1992],)e(The)h(to)n(w) n(ers)f(of)i(Hanoi)f(problem)g(with)h(parallel)704 2889 y(mo)n(v)n(es,)j Fi(Inform.)31 b(Pr)l(o)l(c)l(ess.)f(L)l(ett.)e Fc(44)p Fj(,)f(241{243.)515 2997 y(789.)40 b(J.-S.)28 b(W)-7 b(u)28 b(and)h(R.-J.)e(Chen)i([1993],)d(The)i(to)n(w)n(ers)f(of) h(Hanoi)g(problem)g(with)g(cyclic)704 3097 y(parallel)e(mo)n(v)n(es,)h Fi(Inform.)j(Pr)l(o)l(c)l(ess.)h(L)l(ett.)c Fc(46)p Fj(,)g(1{6.)515 3205 y(790.)40 b(W.)33 b(A.)h(Wytho\013)g([1907],)d(A)i(mo)r (di\014cation)g(of)g(the)h(game)e(of)h(N