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Henning}, TITLE = {Queens graphs}, NOTE = {Combinatorics and number theory (Tiruchirappalli, 1996)}, JOURNAL = {Discrete Math.}, VOLUME = {206}, YEAR = {1999}, PAGES = {63--75}, MRCLASS = {05C75}, MRNUMBER = {MR1665386 (2000f:05066)}, } @article{BBCH2003, author = {A. Bekmetjev and G. Brightwell and A. Czygrinow and G. Hurlbert}, year = 2003, title = {Thresholds for families of multisets, with an application to graph pebbling}, journal = {Discrete Math.}, volume = 269, pages = {21-34}, mrnumber = {MR1989450 (2004i:05152)}, } @book{Bel1960, author = {R. C. Bell}, year = {1960, 1969}, title = {Board and Table Games from Many Civilisations}, volume = {I \& II}, publisher = {Oxford University Press}, note = {revised in 1979, Dover}, } @book{Bel1988, author = {R. Bell and M. Cornelius}, year = 1988, title = {Board Games Round the World: A Resource Book for Mathematical Investigations}, publisher = {Cambridge University Press, Cambridge}, note = {reprinted 1990}, } @article{BFH2001, author = {A. J. Benjamin and M. T. Fluet and M. L. Huber}, year = 2001, title = {Optimal Token Allocations in Solitaire Knock 'm Down}, journal = {Electr. J. Combin.}, volume = {8(2)}, pages = {\#R2, 8pp.}, url = {http://www.combinatorics.org/}, note = {Volume in honor of Aviezri S. Fraenkel}, mrnumber = {MR1853253 (2002g:91048)}, } @article{BMW1991, author = {S. J. Benkoski and M. G. Monticino and J. R. Weisinger}, year = 1991, title = {A survey of the search theory literature}, journal = {Naval Res. Logistics}, volume = 38, pages = {469-494}, } @article{Ben1994, author = {G. Bennett}, year = 1994, title = {Double dipping: the case of the missing binomial coefficient identities}, journal = {Theoret. Comput. Sci. \emph{(Math Games)}}, volume = 123, pages = {351-375}, } @article {Ben1987, AUTHOR = {Bentz, Hans-J.}, TITLE = {Proof of the {B}ulgarian {S}olitaire conjectures}, JOURNAL = {Ars Combin.}, FJOURNAL = {Ars Combinatoria}, VOLUME = {23}, YEAR = {1987}, PAGES = {151--170}, ISSN = {0381-7032}, CODEN = {ACOMDN}, MRCLASS = {05A17 (90D42)}, MRNUMBER = {MR886950 (88k:05018)}, MRREVIEWER = {D. A. Klarner}, } @article {BeSa2006a, AUTHOR = {Berend, Daniel and Sapir, Amir}, TITLE = {The cyclic multi-peg tower of {H}anoi}, JOURNAL = {ACM Trans. Algorithms}, FJOURNAL = {ACM Transactions on Algorithms}, VOLUME = {2}, YEAR = {2006}, PAGES = {297--317}, ISSN = {1549-6325}, MRCLASS = {68Q25 (05A05 68W40)}, MRNUMBER = {**MR2253783, pending}, } @article {BeSa2006b, AUTHOR = {Berend, Daniel and Sapir, Amir}, TITLE = {The diameter of {H}anoi graphs}, JOURNAL = {Inform. Process. Lett.}, FJOURNAL = {Information Processing Letters}, VOLUME = {98}, YEAR = {2006}, PAGES = {79--85}, ISSN = {0020-0190}, CODEN = {IFPLAT}, MRCLASS = {68W40 (05C85 68Q25)}, MRNUMBER = {MR2207581 (2006m:68187)}, MRREVIEWER = {Jean-Paul Allouche}, } @incollection{Ber1981, author = {D. Berengut}, year = 1981, title = {A random hopscotch problem or how to make Johnny read more}, pages = {51-59}, editor = {D. A. Klarner}, publisher = {Wadsworth Internat., Belmont, CA}, booktitle = {The Mathematical Gardner}, } @article{BeGn1984, author = {B. Berezovskiy and A. Gnedin}, year = 1984, title = {The best choice problem}, journal = {Akad. Nauk, USSR, Moscow \emph{(in Russian)}}, } @article {Ber1956, AUTHOR = {Berge, Claude}, TITLE = {La fonction de {G}rundy d'un graphe infini}, JOURNAL = {C. R. Acad. Sci. Paris}, VOLUME = {242}, YEAR = {1956}, PAGES = {1404--1407}, MRCLASS = {90.0X}, MRNUMBER = {MR0089115 (19,621d)}, } @book {Ber1957, AUTHOR = {Berge, C.}, TITLE = {Th\'eorie g\'en\'erale des jeux \`a {$n$} personnes}, SERIES = {M\'emor. Sci. Math., no. 138}, PUBLISHER = {Gauthier-Villars}, ADDRESS = {Paris}, YEAR = {1957}, PAGES = {114}, MRCLASS = {90.00}, MRNUMBER = {MR0099259 (20 \#5700)}, MRREVIEWER = {I. Mann}, } @article{Ber1976, author = {C. Berge}, year = 1976, title = {Sur les jeux positionnels}, journal = {Cahiers du Centre \'Etudes Rech. Op\'er.}, volume = 18, pages = {91-107}, } @incollection{Ber1977, author = {C. Berge}, year = 1977, title = {Vers une th\'eorie g\'en\'erale des jeux positionnels}, editor = {R. Henn and O. Moeschlin}, pages = {13-24}, publisher = {Springer Verlag, Berlin}, volume = 141, booktitle = {Mathematical Economics and Game Theory, Essays in Honor of Oskar Morgenstern, \emph{Lecture Notes in Economics}}, } @incollection{Ber1981a, author = {C. Berge}, year = 1981, title = {Some remarks about a Hex problem}, pages = {25-27}, editor = {D. A. Klarner}, publisher = {Wadsworth Internat., Belmont, CA}, booktitle = {The Mathematical Gardner}, } @article {Ber1982, AUTHOR = {Berge, C.}, TITLE = {Les jeux combinatoires}, JOURNAL = {Cahiers Centre \'Etudes Rech. Op\'er.}, FJOURNAL = {Cahiers du Centre d'\'Etudes de Recherche Op\'erationnelle}, VOLUME = {24}, YEAR = {1982}, PAGES = {89--105}, ISSN = {0008-9737}, CODEN = {CCROAT}, MRCLASS = {90D05 (05B30)}, MRNUMBER = {MR687875 (84d:90112)}, } @inbook{Ber1985, author = {C. Berge}, year = 1985, title = {Graphs}, chapter = 14, publisher = {North-Holland, Amsterdam}, } @inbook{Ber1989, author = {C. Berge}, year = 1989, title = {Hypergraphs}, chapter = 4, publisher = {Elsevier (French: Gauthier Villars 1988)}, } @article {Ber1992, AUTHOR = {Berge, Claude}, TITLE = {Les jeux sur un graphe}, JOURNAL = {Cahiers Centre \'Etudes Rech. Op\'er.}, FJOURNAL = {Cahiers du Centre d'\'Etudes de Recherche Op\'erationnelle. Operations Research, Statistics and Applied Mathematics}, VOLUME = {34}, YEAR = {1992}, PAGES = {95--101}, ISSN = {0774-3068}, CODEN = {CCROAT}, MRCLASS = {05C99 (05C65 90D35)}, MRNUMBER = {MR1226531 (94h:05089)}, MRREVIEWER = {Robin J. Wilson}, } @article{Ber1996, author = {C. Berge}, year = 1996, title = {Combinatorial games on a graph}, journal = {Discrete Math.}, volume = 151, pages = {59-65}, } @article{BeDu1988, author = {C. Berge and P. Duchet}, year = 1988, title = {Perfect graphs and kernels}, journal = {Bull. Inst. Math. Acad. Sinica}, volume = 16, pages = {263-274}, } @article{BeDu1990, author = {C. Berge and P. Duchet}, year = 1990, title = {Recent problems and results about kernels in directed graphs}, journal = {Discrete Math.}, volume = 86, pages = {27-31}, note = {appeared first under the same title in {\it Applications of Discrete Mathematics} (Clemson, SC, 1986), 200--204, SIAM, Philadelphia, PA, 1988}, } @article{BeLa1976, author = {C. Berge and M. {Las Vergnas}}, year = 1976, title = {Un nouveau jeu positionnel, le ``Match-It", ou une construction dialectique des couplages parfaits}, journal = {Cahiers du Centre \'Etudes Rech. Op\'er.}, volume = 18, pages = {83-89}, } @article{BeSc1956, author = {C. Berge and M. P. Sch\"{u}tzenberger}, year = 1956, title = {Jeux de Nim et solutions}, journal = {Acad. Sci. Paris}, volume = 242, pages = {1672-1674}, note = {(French)} } @inproceedings{Ber1972, author = {E. R. Berlekamp}, year = 1972, title = {Some recent results on the combinatorial game called Welter's Nim}, booktitle = {Proc. 6th Ann. Princeton Conf. Information Science and Systems}, pages = {203-204}, } @article{Ber1974, author = {E. R. Berlekamp}, year = 1974, title = {The Hackenbush number system for compression of numerical data}, journal = {Inform. and Control}, volume = 26, pages = {134-140}, } @article{Ber1988a, author = {E. R. Berlekamp}, year = 1988, title = {Blockbusting and domineering}, journal = {J. Combin. Theory \emph{(Ser.~A)}}, volume = 49, pages = {67-116}, note = {an earlier version, entitled Introduction to blockbusting and domineering, appeared in: {\it The Lighter Side of Mathematics}, Proc. E. Strens Memorial Conf. on Recr. Math. and its History, Calgary, 1986, Spectrum Series (R. K. Guy and R. E. Woodrow, eds.), Math. Assoc. of America, Washington, DC, 1994, pp. 137--148}, } @incollection{Ber1990, author = {E. Berlekamp}, year = 1990, title = {Two-person, perfect-information games}, pages = {275-287}, publisher = {Amer. Math. Soc., Providence, RI}, volume = 50, booktitle = {The Le\-ga\-cy of John von Neumann \emph{(Hempstead NY, 1988)}, Proc. Sympos. Pure Math.}, } @incollection{Ber1991, author = {E. R. Berlekamp}, year = 1991, title = {Introductory overview of mathematical Go end\-games}, pages = {73-100}, editor = {R. K. Guy}, publisher = {Amer. Math. Soc., Providence, RI}, volume = 43, booktitle = {Combinatorial Games, \emph{Proc. Symp. Appl. Math.}}, } @incollection{Ber1996a, author = {E. R. Berlekamp}, year = 1996, title = {The economist's view of combinatorial games}, pages = {365-405}, editor = {R. J. Nowakowski}, publisher = {Cambridge University Press, Cambridge}, volume = 29, booktitle = {Games of No Chance, \emph{Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ.}}, } @incollection{Ber2000a, author = {E. R. Berlekamp}, year = 2000, title = {Sums of {$N \times 2$} Amazons}, volume = {35}, pages = {1-34}, editor = {{F.T. Bruss} and {L.M. Le Cam}}, publisher = {Beechwood, Ohio: Institute of Mathematical Statistics}, booktitle = {Institute of Mathematical Statistics Lecture Notes--Monograph Series}, note = {Papers in honor of Thomas S. Ferguson}, mrnumber = {MR1833848 (2002e:91033)}, } @book{Ber2000b, author = {E. R. Berlekamp}, year = 2000, title = {The Dots-and-Boxes Game: Sophisticated Child's Play}, volume = {}, publisher = {A K Peters, Natick, MA}, mrnumber = {MR1780088 (2001i:00005)}, } @article{Ber2002, author = {E. R. Berlekamp}, year = 2002, title = {Four games for Gardner}, journal = {{\rm in:} Puzzler's Tribute: a Feast for the Mind{\rm ,}}, chapter = {}, pages = {383-386}, note = {honoring Martin Gardner (D. Wolfe and T. Rodgers, eds.), A K Peters, Natick, MA}, publisher = {}, } @incollection{Ber2002b, author = {E. R. Berlekamp}, year = 2002, title = {Idempotents among partisan games}, pages = {3-23}, editor = {R. J. Nowakowski}, publisher = {Cambridge University Press, Cambridge}, volume = {42}, booktitle = {More Games of No Chance, \emph{Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ.}}, } @incollection{Ber2002a, author = {E. R. Berlekamp}, year = 2002, title = {The 4G4G4G4G4 problems and solutions}, pages = {231-241}, editor = {R. J. Nowakowski}, publisher = {Cambridge University Press, Cambridge}, volume = {42}, booktitle = {More Games of No Chance, \emph{Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ.}}, } @book{BCG2001, author = {E. R. Berlekamp and J. H. Conway and R. K. Guy}, year = {2001-2004}, title = {Winning Ways for your Mathematical Plays}, volume = {1-4}, publisher = {A K Peters, Wellesley, MA}, note = {2nd edition: vol. 1 (2001), vols. 2, 3 (2003), vol. 4 (2004); translation of 1st edition (1982) into German: {\it Gewinnen, Strategien f\"ur Mathematische Spiele} by G. Seiffert, Foreword by K. Jacobs, M. Rem\'enyi and Seiffert, Friedr. Vieweg \& Sohn, Braunschweig (four volumes), 1985}, } @incollection{BeKi1996, author = {E. R. Berlekamp and Y. Kim}, year = 1996, title = {Where is the ``Thousand-Dollar Ko?''}, pages = {203-226}, editor = {R. J. Nowakowski}, publisher = {Cambridge University Press, Cambridge}, volume = 29, booktitle = {Games of No Chance, \emph{Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ.}}, } @book{BeRo1999, editor = {E. Berlekamp and T. Rodgers}, year = 1999, title = {The Mathemagician and Pied Puzzler}, publisher = {A K Peters, Natick, MA}, note = {A collection in tribute to Martin Gardner. Papers from the Gathering for Gardner Meeting (G4G1) held in Atlanta, GA, January 1993}, } @incollection{BeSc2002, author = {E. Berlekamp and K. Scott}, year = 2002, title = {Forcing your opponent to stay in control of a loony dots-and-boxes endgame}, pages = {317-330}, editor = {R. J. Nowakowski}, publisher = {Cambridge University Press, Cambridge}, volume = {42}, booktitle = {More Games of No Chance, \emph{Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ.}}, mrnumber = {MR1973020}, } @book{BeWo1994, author = {E. Berlekamp and D. Wolfe}, year = 1994, title = {Mathematical Go --- Chilling Gets the Last Point}, publisher = {A K Peters, Natick, MA}, } @book{Ber1976a, author = {P. Berloquin}, year = 1976, title = {100 Jeux de Table}, publisher = {Flammarion, Paris}, } @book{Ber1995, author = {P. Berloquin}, year = 1995, title = {100 Games of Logic}, publisher = {Barnes \& Noble}, } @book{Ber1999, author = {{P. Berloquin and D. Dugas (Illustrator)}}, year = 1999, title = {100 Perceptual Puzzles}, publisher = {Barnes \& Noble}, } @incollection{BDDFJM2002, author = {T. C. Biedl and E. D. Demaine and M. L. Demaine and R. Fleischer and L. Jacobsen and I. Munro}, year = 2002, title = {The complexity of Clickomania}, pages = {389-404}, editor = {R. J. Nowakowski}, publisher = {Cambridge University Press, Cambridge}, volume = {42}, booktitle = {More Games of No Chance, \emph{Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ.}}, mrnumber = {MR1973107 (2004b:91041)}, } @article{Big1999, author = {N. L. Biggs}, year = 1999, title = {Chip-firing and the critical group of a graph}, journal = {J. Algebr. Comb.}, volume = 9, pages = {25-45}, } @book{Bin1992, author = {K. Binmore}, year = 1992, title = {Fun and Games: a Text on Game Theory}, publisher = {D.C. Heath, Lexington}, } @article{BiGo1992, author = {J. Bitar and E. Goles}, year = 1992, title = {Parallel chip firing games on graphs}, journal = {Theoret. Comput. Sci.}, volume = 92, pages = {291-300}, } @article{BjLo1992, author = {A. Bj\"orner and L. Lov\'asz}, year = 1992, title = {Chip-firing games on directed graphs}, journal = {J. Algebraic Combin.}, volume = 1, pages = {305-328}, } @article{BLC1991, author = {A. Bj\"orner and L. Lov\'asz and P. Chor}, year = 1991, title = {Chip-firing games on graphs}, journal = {European J. Combin.}, volume = 12, pages = {283-291}, } @article{BlKi2001, author = {N. M. Blachman and D. M. Kilgour}, year = 2001, title = {Elusive optimality in the box problem}, journal = {Math. Mag.}, volume = 74, number = 3, pages = {171-181}, mrnumber = {MR2104911. There will be no review of this item}, } @book{BlGi1954, author = {D. Blackwell and M. A. Girshick}, year = 1954, title = {Theory of Games and Statistical Decisions}, publisher = {Wiley, New York, NY}, } @article{BDG2006, author = {L. Blanc and E. Duch\^{e}ne and S. Gravier}, year = 2006, title = {A deletion game on graphs: ๔le pic ar\^{e}te๖}, journal = {INTEGERS, Electr. J. of Combinat. Number Theory}, volume = 6, pages = {\#G02, 10pp., Comb. Games Sect.}, url = {http://www.integers-ejcnt.org/vol5.html}, MRNUMBER = {MR2215359. There will be no review of this item}, } @article{BlFr1990, author = {U. Blass and A. S. Fraenkel}, year = 1990, title = {The Sprague--Grundy function for Wyt\-hoff's game}, journal = {Theoret. Comput. Sci. \emph{(Math Games)}}, volume = 75, pages = {311-333}, } @article{BFG1998, author = {U. Blass and A. S. Fraenkel and R. Guelman}, title = {How far can Nim in disguise be stretched?}, journal = {J. Combin. Theory \emph{(Ser.~A)}}, volume = 84, pages = {145-156}, year = 1998, mrnumber = {MR1652900 (2000d:91029)}, } @article{Bli1986, author = {M. Blidia}, year = 1986, title = {A parity digraph has a kernel}, journal = {Combinatorica}, volume = 6, pages = {23-27}, } @article{BDJMM1999, author = {M. Blidia and P. Duchet and H. Jacob and F. Maffray and H.. Meyniel}, year = 1999, title = {Some operations preserving the existence of kernels}, journal = {Discrete Math.}, volume = 205, pages = {211-216}, } @article{BDM1993, author = {M. Blidia and P. Duchet and F. Maffray}, year = 1993, title = {On kernels in perfect graphs}, journal = {Combinatorica}, volume = 13, pages = {231-233}, } @article{BoHa1998, author = {J-P. Bode and H. Harborth}, year = 1998, title = {Achievement games on Platonic solids}, journal = {Bull. Inst. Combin. Appl.}, volume = 23, pages = {23-32}, mrnumber = {MR1621748 (99d:05020)}, } @article{BoHa2000a, author = {J-P. Bode and H. Harborth}, year = 2000, title = {Hexagonal polyomino achievement}, journal = {Discrete Math.}, volume = 212, pages = {5-18}, mrnumber = {MR1748669 (2000k:05082)}, } @article{BoHa2000b, author = {J-P. Bode and H. Harborth}, year = 2000, title = {Independent chess pieces on Euclidean boards}, journal = {J. Combin. Math. Combin. Comput.}, volume = 33, pages = {209-223}, mrnumber = {MR1772763 (2001c:05105)}, } @article{BoHa2000c, author = {J-P. Bode and H. Harborth}, year = 2000, title = {Triangular mosaic polyomino achievement}, journal = {Congr. Numer.}, volume = 144, pages = {143-152}, note = {Proc. 31st Southeastern Internat. Conf. on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 2000)}, mrnumber = {MR1817929 (2001m:05082)}, } @article{BoHa2001, author = {J-P. Bode and H. Harborth}, year = 2001, title = {Triangle polyomino set achievement}, journal = {Congr. Numer.}, volume = 148, pages = {97--101}, note = {Proc.32nd Southeastern Internat. Conf. on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 2002)}, mrnumber = {MR1887377 (2002k:05057)}, } @article{BoHa2002, author = {J-P. Bode and H. Harborth}, year = 2002, title = {Triangle and hexagon gameboard Ramsey numbers}, journal = {Congr. Numer.}, volume = 158, pages = {93-98}, note = {Proc.33rd Southeastern Internat. Conf. on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 2002)}, mrnumber = {MR1985149 (2004d:05129)}, } @article{BoHa2003a, author = {J-P. Bode and H. Harborth}, year = 2003, title = {Independence for knights on hexagon and triangle boards}, journal = {Discrete Math.}, volume = 272, pages = {27-35}, mrnumber = {MR2019197 (2004i:05115)}, } @article{BHH2003b, author = {J-P. Bode and H. Harborth and M. Harborth}, year = 2003, title = {King independence on triangle boards}, journal = {Discrete Math.}, volume = 266, pages = {101-107}, note = {Presented at 18th British Combinatorial Conference (Brighton, 2001)}, mrnumber = {MR1991709 (2004f:05129)}, } @article{BoHa2004, author = {J-P. Bode and H. Harborth and M. Harborth}, year = 2004, title = {King graph Ramsey numbers}, journal = {J. Combin. Math. Combin. Comput.}, volume = 50, pages = {47-55}, mrnumber = {MR2075855. There will be no review of this item}, } @article{BoHa1999, author = {J-P. Bode and H. Harborth and H. Weiss}, year = 1999, title = {Independent knights on hexagon boards}, journal = {Congr. Numer.}, volume = 141, pages = {31-35}, note = {Proc. 30th Southeastern Internat. Conf. on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1999)}, mrnumber = {MR1745222 (2000k:05201)}, } @article{BoHi1999, author = {J-P. Bode and A. M. Hinz}, year = 1999, title = {Results and open problems on the Tower of Hanoi}, journal = {Congr. Numer.}, volume = 139, pages = {113-122}, note = {Proc.30th Southeastern Internat. Conf. on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1999)}, } @article{Bod1991, author = {H. L. Bodlaender}, year = 1991, title = {On the complexity of some coloring games}, journal = {Internat. J. Found. Comput. Sci.}, volume = 2, pages = {133-147}, mrnumber = {MR1143920 (92j:68042)}, } @article{Bod1993, author = {H. L. Bodlaender}, year = 1993, title = {Complexity of path forming games}, journal = {Theoret. Comput. Sci. \emph{(Math Games)}}, volume = 110, pages = {215-245}, } @incollection{Bod1993a, author = {H. L. Bodlaender}, year = 1993, title = {Kayles on special classes of graphs---an application of Sprague-Grundy theory}, pages = {90-102}, publisher = {Springer, Berlin}, volume = 657, booktitle = {Graph-Theoretic Concepts in Computer Science \emph{(Wiesbaden-Naurod, 1992)}, \emph{Lecture Notes in Comput. Sci.}}, mrnumber = {MR1244129 (94i:90189)}, } @article{BoKr1992, author = {H. L. Bodlaender and D. Kratsch}, year = 1992, title = {The complexity of coloring games on perfect graphs}, journal = {Theoret. Comput. Sci. \emph{(Math Games)}}, volume = 106, pages = {309-326}, } @article{BoKr2002, author = {H. L. Bodlaender and D. Kratsch}, year = 2002, title = {Kayles and nimbers}, journal = {J. Algorithms}, volume = 43, pages = {106-119}, mrnumber = {MR1900711 (2003d:05201)}, } @article{BHK2001, author = {T. Bohman and R. Holzman and D. Kleitman}, year = 2001, title = {Six Lonely Runners}, journal = {Electr. J. 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Combinatorics}, volume = 1, pages = {\#R5, 13pp.}, url = {http://www.combinatorics.org/}, } @incollection{Fra1994a, author = {A. S. Fraenkel}, year = 1994, title = {Recreation and depth in combinatorial games}, pages = {176-194}, editor = {R. K. Guy and R. E. Woodrow}, publisher = {Math. Assoc. of America, Washington, DC}, booktitle = {The Lighter Side of Mathematics, \emph{Proc. E. Strens Memorial Conf. on Recr. Math. and its History, Calgary, 1986, Spectrum Series}}, } @incollection{Fra1996, author = {A. S. Fraenkel}, year = 1996, title = {Error-correcting codes derived from combinatorial games}, pages = {417-431}, editor = {R. J. Nowakowski}, publisher = {Cambridge University Press, Cambridge}, volume = 29, booktitle = {Games of No Chance, \emph{Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ.}}, } @incollection{Fra1996a, author = {A. S. Fraenkel}, year = 1996, title = {Scenic trails ascending from sea-level Nim to alpine chess}, pages = {13-42}, editor = {R. J. Nowakowski}, publisher = {Cambridge University Press, Cambridge}, volume = 29, booktitle = {Games of No Chance, \emph{Proc. MSRI Workshop on Combinatorial Games, July, 1994, Berkeley, CA, MSRI Publ.}}, } @article{Fra1997, author = {A. S. Fraenkel}, year = 1997, title = {Combinatorial game theory foundations applied to digraph kernels}, journal = {Electr. J. Combinatorics}, volume = 4, number = {2}, pages = {\#R10, 17pp.}, note = {Volume in honor of Herbert Wilf}, url = {http://www.combinatorics.org/}, } @article{Fra1998a, author = {A. S. Fraenkel}, year = 1998, title = {Heap games, numeration systems and sequences}, journal = {Ann. Comb.}, volume = 2, pages = {197-210}, note = {an earlier version appeared in: {\em Fun With Algorithms\/}, Vol.~4 of {\it Proceedings in Informatics\/} (E. Lodi, L. Pagli and N. Santoro, eds.), Carleton Scientific, University of Waterloo, Waterloo, Ont., pp. 99--113, 1999. Conference took place on the island of Elba, June 1998.}, mrnumber = {MR1681514 (2000b:91001)}, } @article{Fra1998b, author = {A. S. Fraenkel}, year = 1998, title = {Multivision: an intractable impartial game with a linear winning strategy}, journal = {Amer. Math. Monthly}, volume = 105, pages = {923-928}, } @article{Fra2000, author = {A. S. Fraenkel}, year = 2000, title = {Recent results and questions in combinatorial game complexities}, journal = {Theoret. Comput. Sci.}, volume = 249, pages = {265-288}, note = {Conference version in: Proc. AWOCA98 --- Ninth Australasian Workshop on Combinatorial Algorithms, C.S. Iliopoulos, ed., Perth, Western Australia, 27--30 July, 1998, special AWOCA98 issue, pp. 124-146}, mrnumber = {MR1798313 (2001j:91033)}, } @inproceedings{Fra2001, author = {A. S. Fraenkel}, year = 2001, title = {Virus versus mankind}, booktitle = {Proc.\ 2nd Intern.\ Conference on Computers and Games CG'2000}, organization = {Hamamatsu, Japan, Oct.\ 2000, Lecture Notes in Computer Science, Springer}, volume= {2063}, pages = {204--213}, editor = {T. Marsland and I. Frank}, } @article{Fra2002a, author = {A. S. Fraenkel}, year = 2002, title = {Mathematical chats between two physicists}, journal = {{\rm in:} Puzzler's Tribute: a Feast for the Mind{\rm ,}}, chapter = {}, note = {honoring Martin Gardner (D. Wolfe and T. Rodgers, eds.), A K Peters, Natick, MA, pp. 383-386}, publisher = {}, } @article{Fra2002b, author = {A. S. Fraenkel}, year = 2002, title = {Arrays, numeration systems and Frankenstein games}, journal = {Theoret. Comput. Sci.}, volume = 282, pages = {271-284}, note = {special`` Fun With Algorithms" issue}, mrnumber = {MR1909052 (2003h:91036)}, } @incollection{Fra2002c, author = {A. S. Fraenkel}, year = 2002, title = {Two-player games on cellular automata}, pages = {279-306}, editor = {R. J. Nowakowski}, publisher = {Cambridge University Press, Cambridge}, volume = {42}, booktitle = {More Games of No Chance, \emph{Proc. MSRI Workshop on Combinatorial Games, July, 2000, Berkeley, CA, MSRI Publ.}}, mrnumber = {MR1973018 (2004b:91004)}, } @article{Fra2004a, author = {A. S. Fraenkel}, year = 2004, title = {Complexity, appeal and challenges of combinatorial games}, journal = {Theoret. Comp. Sci.}, volume = {313}, pages = {393-415}, note = {Expanded version of a keynote address at Dagstuhl Seminar ``Algorithmic Combinatorial Game Theory'', Feb. 2002, special issue on Algorithmic Combinatorial Game Theory}, mrnumber = {MR2056935. There will be no review of this item}, } @article{Fra2004b, author = {A. S. Fraenkel}, year = 2004, title = {New games related to old and new sequences}, journal = {INTEGERS, Electr. J of Combinat. Number Theory}, volume = {4}, pages = {\#G6, 18pp., Comb. Games Sect.}, url = {http://www.integers-ejcnt.org/vol4.html}, note = {1st version in Proc.10-th Advances in Computer Games (ACG-10 Conf.), H. J. van den Herik, H. Iida and E. A. Heinz eds., Graz, Austria, Nov.\ 2003, Kluwer, pp. 367-382}, mrnumber = {MR2042724}, } @article{Fra2005, author = {A. S. Fraenkel}, year = 2005, title = {Euclid and Wythoff games}, journal = {Discrete Math.}, volume = {304}, pages = {65-68}, mrnumber = {MR2184445 (2006f:91006)}, } @article{Fra2006a, author = {A. S. Fraenkel}, year = 2006, title = {Games played by Boole and Galois}, journal = {Discrete Appl. Math.}, volume = {}, pages = {}, note = {to appear in special issue honoring Peter Hammer}, } @article{Fra2006b, author = {A. S. Fraenkel}, year = 2006, title = {Nim is easy, chess is hard --- but why??}, journal = {J. Internat. Computer Games Assoc.}, volume = {}, issue = {40}, pages = {}, note = {to appear; earlier version appeared in Plus Mag. {\rm (}electronic{\rm )}, pluschat section,\hfill\break http://plus.maths.org/issue40/editorial/index.html}, } @article{Fra2007a, author = {A. S. Fraenkel}, year = 2007, title = {The Raleigh game}, journal = {INTEGERS, Electr. J. of Combinat. Number Theory}, volume = 7, pages = {}, note = {special volume in honor of Ron Graham, to appear}, } @article{Fra2007b, author = {A. S. Fraenkel}, year = 2007, title = {Why are games exciting and stimulating?}, journal = {Math Horizons}, volume = {}, pages = {}, note = {to appear in a special issue focusing on mathematics and games}, } @article{FrBo1973, author = {A. S. Fraenkel and I. Borosh}, year = 1973, title = {A generalization of Wythoff's game}, journal = {J. Combin. Theory \emph{(Ser.~A)}}, volume = 15, pages = {175-191}, } @inproceedings{FGJSY1978, author = {A. S. Fraenkel and M. R. Garey and D. S. Johnson and T. Schaefer and Y. Yesha}, year = 1978, title = {The complexity of checkers on an $n\times n$ board --- preliminary report}, booktitle = {Proc. 19th Ann. Symp. Foundations of Computer Science \emph{(Ann Arbor, MI, Oct. 1978)}}, organization = {IEEE Computer Soc., Long Beach, CA}, pages = {55-64}, } @article{FrGo1987, author = {A. S. Fraenkel and E. Goldschmidt}, year = 1987, title = {Pspace-hardness of some combinatorial games}, journal = {J. Combin. Theory \emph{(Ser.~A)}}, volume = 46, pages = {21-38}, } @article{FrHa1989, author = {A. S. Fraenkel and F. Harary}, year = 1989, title = {Geodetic contraction games on graphs}, journal = {Internat. J. Game Theory}, volume = 18, pages = {327-338}, } @article{FrHe1980, author = {A. S. Fraenkel and H. Herda}, year = 1980, title = {Never rush to be first in playing Nimbi}, journal = {Math. Mag.}, volume = 53, pages = {21-26}, } @article{FJKS1995, author = {A. S. Fraenkel and A. Jaffray and A. Kotzig and G. Sabidussi}, year = 1995, title = {Modular Nim}, journal = {Theoret. Comput. Sci. \emph{(Math Games)}}, volume = 143, pages = {319-333}, } @article {FrKi1994, AUTHOR = {Fraenkel, A. S. and Kimberling, Clark}, TITLE = {Generalized {W}ythoff arrays, shuffles and interspersions}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {126}, YEAR = {1994}, PAGES = {137--149}, ISSN = {0012-365X}, CODEN = {DSMHA4}, MRCLASS = {11B83 (05A99)}, MRNUMBER = {MR1264482 (95c:11028)}, MRREVIEWER = {Volker Strehl}, } @article{FrKo2007, author = {A. S. Fraenkel and A. Kontorovich}, year = 2007, title = {The Sierpi\'{n}ski sieve of Nim-varieties and binomial coefficients}, journal = {INTEGERS, Electr. J. of Combinat. Number Theory}, volume = 7, pages = {special volume in honor of Ron Graham}, note = {to appear}, } @article{FrKo1987, author = {A. S. Fraenkel and A. Kotzig}, year = 1987, title = {Partizan octal games: partizan subtraction games}, journal = {Internat. J. Game Theory}, volume = 16, pages = {145-154}, } @article{FrKr2004, author = {A. S. Fraenkel and D. Krieger}, year = 2004, title = {The structure of complementary sets of integers: a 3-shift theorem}, journal = {Internat. J. Pure and Appl. Math.}, volume = {10}, pages = {1-49}, mrnumber = {MR2020683 (2004h:05012)}, } @article{FrLi1981, author = {A. S. Fraenkel and D. Lichtenstein}, year = 1981, title = {Computing a perfect strategy for $n\times n$ chess requires time exponential in $n$}, journal = {J. Combin. Theory \emph{(Ser.~A)}}, volume = 31, pages = {199-214}, MRNUMBER = {MR629595 (83b:68044)}, note = {preliminary version in Proc. 8th Internat. Colloq. Automata, Languages and Programming (S. Even and O. Kariv, eds.), Vol. 115, Acre, Israel, 1981, Lecture Notes in Computer Science, Springer Verlag, Berlin, pp. 278--293}, } @article{FLN1988, author = {A. S. Fraenkel and M. Loebl and J. Ne\v{s}et\v{r}il}, year = 1988, title = {Epidemiography II.~Games with a dozing yet winning player}, journal = {J. Combin. Theory \emph{(Ser.~A)}}, volume = 49, pages = {129-144}, } @article{FrLo1989, author = {A. S. Fraenkel and M. Lorberbom}, year = 1989, title = {Epidemiography with various growth functions}, journal = {Discrete Appl. Math.}, volume = 25, pages = {53-71}, note = {special issue on Combinatorics and Complexity} } @article{FrLo1991, author = {A. S. Fraenkel and M. Lorberbom}, year = 1991, title = {Nimhoff games}, journal = {J. Combin. Theory \emph{(Ser.~A)}}, volume = 58, pages = {1-25}, } @article{FrNe1985, author = {A. S. Fraenkel and J. Ne\v{s}et\v{r}il}, year = 1985, title = {Epidemiography}, journal = {Pacific J. Math.}, volume = 118, pages = {369-381}, } @article{FrOz1998, author = {A. S. Fraenkel and M. Ozery}, year = 1998, title = {Adjoining to Wythoff's game its $P$-positions as moves}, journal = {Theoret. Comput. Sci.}, volume = 205, pages = {283-296}, } @article{FrPe1975, author = {A. S. Fraenkel and Y. Perl}, year = 1975, title = {Constructions in combinatorial games with cycles}, journal = {Coll. Math. Soc. J\'anos Bolyai}, volume = 10, note = {Proc. Internat. Colloq. on Infinite and Finite Sets, Vol.~2 (A. Hajnal, R. Rado and V. T. S\'os, eds.) Keszthely, Hungary, 1973, North-Holland}, pages = {667-699}, } @article{FrRa2001, author = {A. S. Fraenkel and O. Rahat}, year = 2001, title = {Infinite cyclic impartial games}, journal = {Theoret. Comput. Sci.}, volume = 252, publisher = {Springer}, pages = {13-22}, note = {special "Computers and Games" issue; first version appeared in Proc. 1st Intern. Conf. on Computer Games CG'98, {\rm Tsukuba, Japan, Nov. 1998,} \emph{Lecture Notes in Computer Science}, Vol. 1558, Springer, pp. 212-221, 1999.}, mrnumber = {MR1715689 (2000m:91028)}, } @inproceedings{FrRa2003, author = {A. S. Fraenkel and O. Rahat}, year = 2003, title = {Complexity of error-correcting codes derived from combinatorial games}, booktitle = {Proc. Intern. Conference on Computers and Games CG'2002, Edmonton, Alberta, Canada, July 2002,}, editor = {Y. Bj\"{o}rnsson and M. M\"{u}ller and J. Schaeffer}, volume = {LNCS 2883}, pages = {201-21}, publisher = {Lecture Notes in Computer Science, Springer}, } @article{FrSc1991, author = {A. S. Fraenkel and E. R. Scheinerman}, year = 1991, title = {A deletion game on hypergraphs}, journal = {Discrete Appl. Math.}, volume = 30, pages = {155-162}, } @article{FSU1993, author = {A. S. Fraenkel and E. R. Scheinerman and D. Ullman}, year = 1993, title = {Undirected edge geography}, journal = {Theoret. Comput. Sci. \emph{(Math Games)}}, volume = 112, pages = {371-381}, } @article{FrSi1993, author = {A. S. Fraenkel and S. Simonson}, year = 1993, title = {Geography}, journal = {Theoret. Comput. Sci. \emph{(Math Games)}}, volume = 110, pages = {197-214}, } @article{FrTa1975, author = {A. S. Fraenkel and U. Tassa}, year = 1975, title = {Strategy for a class of games with dynamic ties}, journal = {Comput. Math. Appl.}, volume = 1, pages = {237-254}, } @article{FrTa1982, author = {A. S. Fraenkel and U. Tassa}, year = 1982, title = {Strategies for compounds of