Title: Games of No Chance III

Editors: M. H.  Albert and R. J. Nowakowski


M. H. Albert, R. E. L. Aldred, M. D. Atkinson, C. C. Handley,
D. A. Holton, D. J. McCaughan, and B. E. Sagan, Monotonic Sequence Games.

Elwyn Berlekamp, Yellow Brown Hackenbush

Tristan Cazenave, The use of direct threats in a Monte-Carlo Go program

Erik D. Demaine, Playing Games with Algorithms:
Algorithmic Combinatorial
Game Theory.

Erik D. Demaine , Martin L. Demaine , Rudolf Fleischer,
Robert A. Hearn , and Timo von Oertzen, The Complexity of Dyson Telescopes.

Lim Yew Jin and Jurg Nievergelt, Tigers and Goats is a draw

Adam Duffy, Garrett Kolpin, and David Wolfe, Ordinal Partizan End Nim

Aviezri S. Fraenkel , Elnatan Reisner, The game of End-Wythoff.

Eric J. Friedman, Adam S. Landsberg, On the Geometry of Combinatorial Games:
A renormalization approach

J. P. Grossman, Aaron N. Siegel, Reductions of Partizan Games.

Ryan B. Hayward, A puzzling Hex primer

Robert A. Hearn,  Amazons, Konane, and Cross Purposes are PSPACE-complete
Thane Plambeck, Advances in Losing.

G. A. Mesdal III, Partizan Splittles

Teigo Nakamura, On Counting Liberties in Capturing Races of Go

 Gabriel Nivasch, More on the Sprague?Grundy function for
Wythoff ?s game

 Aaron N. Siegel, Loopy Games

Aaron N. Siegel, Coping with Cycles

Aaron N. Siegel, Backsliding Toads and Frogs

Thomas Wolf , A library of eyes in Go  I: A life & death definition consistent with ?bent-4?

Thomas Wolf , A library of eyes in Go II: Monolithic eyes

D. Wolfe, on day $n$.

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    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.}},
}

@incollection{Ber2008,
  author = {E. R. Berlekamp},
  year = 2008,
  title = {Yellow brown Hackenbush},
  pages = {},
  editor = {M. H. Albert and R. J. Nowakowski},
  publisher = {Cambridge University Press, Cambridge},
  volume = {},
  booktitle = {Games of No Chance III, \emph{Proc. BIRS Workshop on
Combinatorial Games, July, 2005, Banff, Alberta, Canada, 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)},
}

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  pages = {25-45},
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@book{Bin1992,
  author = {K. Binmore},
  year = 1992,
  title = {Fun and Games: a Text on Game Theory},
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@article{BiGo1992,
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  pages = {291-300},
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@article{BLC1991,
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    AUTHOR = {Bj{\"o}rnsson, Yngvi and Hayward, Ryan and Johanson, Michael
              and van Rijswijck, Jack},
     TITLE = {Dead cell analysis in {H}ex and the {S}hannon game},
 BOOKTITLE = {Graph theory in Paris},
    SERIES = {Trends Math.},
     PAGES = {45--59},
 PUBLISHER = {Birkh\"auser},
   ADDRESS = {Basel},
      YEAR = {2007},
   MRCLASS = {91A46 (05C99)},
  MRNUMBER = {MR2279166 (2007j:91023)},
MRREVIEWER = {Kimmo Eriksson},
}

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  year = 2001,
  title = {Elusive optimality in the box problem},
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  number = 3,
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@book{BlGi1954,
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@article{BDG2006,
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  MRNUMBER = {MR2215359},
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@article {BlFr1990,
    AUTHOR = {Blass, Uri and Fraenkel, Aviezri S.},
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    VOLUME = {75},
      YEAR = {1990},
    NUMBER = {3},
     PAGES = {311--333},
      ISSN = {0304-3975},
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MRREVIEWER = {Jos Potters},
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@article{BDJMM1999,
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@article{BoHa2000b,
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@article{BoHa2000c,
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@article{BoHa2001,
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  year = 2001,
  title = {Triangle polyomino set achievement},
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  pages = {97--101},
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@article{BoHa2002,
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Graph Theory and Computing (Boca Raton, FL, 2002)},
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}

@article{BoHa2003a,
  author = {J-P. Bode and H. Harborth},
  year = 2003,
  title = {Independence for knights on hexagon and triangle boards},
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@article{BHH2003b,
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  year = 2003,
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  pages = {101-107},
  note = {Presented at 18th British Combinatorial Conference (Brighton, 2001)},
  mrnumber = {MR1991709 (2004f:05129)},
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@article{BoHa2004,
  author = {J-P. Bode and H. Harborth and M. Harborth},
  year = 2004,
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  volume = 50,
  pages = {47-55},
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@article{BoHa1999,
  author = {J-P. Bode and H. Harborth and H. Weiss},
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  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},
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  volume = 139,
  pages = {113-122},
  note = {Proc.30th Southeastern Internat. Conf.
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@incollection{Bod1993a,
  author = {H. L. Bodlaender},
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  mrnumber = {MR1244129 (94i:90189)},
}

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  pages = {309-326},
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  volume = {8(2)},
  pages = {\#R3, 49 pp.},
  url = {http://www.combinatorics.org/},
  note = {Volume in honor of Aviezri S. Fraenkel},
  mrnumber = {MR1853254 (2002g:11095)},
}

@article{Bok1984,
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  journal = {J. Combin. Theory \emph{(Ser.~A)}},
  volume = {},
  pages = {},
  note = {to appear},
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@article{Boo1998,
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@article{Bor1921,
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@article{BoGu1996,
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@article{BoGu1998,
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@article {BoGu2006,
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  year = 1995,
  title = {Tournament games and positive tournaments},
  journal = {J. Graph Theory},
  volume = 19,
  pages = {217-236},
}

@article{FiNo2001,
  author = {S. L. Fitzpatrick and R. J. Nowakowski},
  year = 2001,
  title = {Copnumber of graphs with strong isometric dimension two},
  journal = {Ars Combin.},
  volume = 59,
  pages = {65-73},
  mrnumber = {MR1832198 (2002b:05053)},
}

@article{FlBa2002,
  author = {G. W. Flake and E. B. Baum},
  year = 2002,
  title = {{\it Rush Hour\/} is PSPACE-complete, or "Why you should
generously tip parking lot attendants"},
  journal = {Theoret. Comput. Sci. \emph{(Math Games)}},
  volume = 270,
  pages = {895-911},
  mrnumber = {MR1871102 (2002h:68068)},
}

@phdthesis{Fla1996,
  author = {A. Flammenkamp},
  year = 1996,
  title = {Lange Perioden in Subtraktions-Spielen},
  school= {University of Bielefeld},
}

@article{FHR2003,
  author = {A. Flammenkamp and A. Holshouser and H. Reiter},
  year = 2003,
  title = {Dynamic one-pile blocking Nim},
  journal = {Electr. J. Combinatorics},
  volume = 10,
  pages = {\#N4, 6 pp.},
  url = {http://www.combinatorics.org/},
  mrnumber = {MR1975777 (2004b:05027)},
}

@article{Fla1978,
  author = {J. A. Flanigan},
  year = 1978,
  title = {Generalized two-pile Fibonacci nim},
  journal = {Fibonacci Quart.},
  volume = 16,
  pages = {459-469},
}

@article{Fla1981,
  author = {J. A. Flanigan},
  year = 1981,
  title = {On the distribution of winning moves in random game trees},
  journal = {Bull. Austr. Math. Soc.},
  volume = 24,
  pages = {227-237},
}

@article{Fla1981a,
  author = {J. A. Flanigan},
  year = 1981,
  title = {Selective sums of loopy partizan graph games},
  journal = {Internat. J. Game Theory},
  volume = 10,
  pages = {1-10},
}

@article{Fla1982,
  author = {J. A. Flanigan},
  year = 1982,
  title = {A complete analysis of black-white Hackendot},
  journal = {Internat. J. Game Theory},
  volume = 11,
  pages = {21-25},
}

@article{Fla1982a,
  author = {J. A. Flanigan},
  year = 1982,
  title = {One-pile time and size dependent take-away games},
  journal = {Fibonacci Quart.},
  volume = 20,
  pages = {51-59},
}

@article{Fla1983,
  author = {J. A. Flanigan},
  year = 1983,
  title = {Slow joins of loopy games},
  journal = {J. Combin. Theory \emph{(Ser.~A)}},
  volume = 34,
  pages = {46-59},
}

@inproceedings{FlTr2006,
  author = {R. Fleischer and G. Trippen},
  title = {Kayles on the way to the stars},
  booktitle = {Proc.\ 4th Intern.\ Conference on Computers and
Games CG'2004},
  organization = {Bar-Ilan University, Ramat-Gan, Israel, July 2004, Lecture Notes in Computer
Science Vol. 3846, Springer},
  year = 2006,
  volume= {},
  editor = {H. J. van den Herik and Y. Bj\"ornsson and N. S. Netanyahu},
  pages = {232-245},
}

@article{Fly1973,
  author = {J. O. Flynn},
  year = 1973,
  title = {Lion and man: the boundary constraint},
  journal = {SIAM J. Control},
  volume = 11,
  pages = {397-411},
}

@article{Fly1974a,
  author = {J. O. Flynn},
  year = 1974,
  title = {Lion and man: the general case},
  journal = {SIAM J. Control},
  volume = 12,
  pages = {581-597},
}

@article{Fly1974b,
  author = {J. O. Flynn},
  year = 1974,
  title = {Some results on max-min pursuit},
  journal = {SIAM J. Control},
  volume = 12,
  pages = {53-69},
}

@article{Fom1998,
  author = {F. V. Fomin},
  year = 1998,
  title = {Helicopter search problems, bandwidth and pathwidth},
  journal = {Discrete Appl. Math.},
  volume = 85,
  pages = {59-70},
}

@article{Fom1999,
  author = {F. V. Fomin},
  year = 1999,
  title = {Note on a helicopter search problem on graphs},
  journal = {Discrete Appl. Math.},
  volume = 95,
  pages = {241-249},
  note = {Proc. Conf. on Optimal Discrete Structures and Algorithms ---
ODSA '97 (Rostock)}
}

@article{FoPe1996,
  author = {F. V. Fomin and N. N. Petrov},
  year = 1996,
  title = {Pursuit-evasion and search problems on graphs},
  journal = {Congr. Numer.},
  volume = 122,
  pages = {47-58},
  note = {Proc. 27-th Southeastern Intern. Conf. on Combinatorics,
Graph Theory and Computing (Baton Rouge, LA, 1996)}
}

@article{FoJo1984,
  author = {L. R. Foulds and D. G. Johnson},
  year = 1984,
  title = {An application of graph theory and integer programming:
chessboard non-attacking puzzles},
  journal = {Math. Mag.},
  volume = 57,
  pages = {95-104},
}

@incollection{Fra1974,
  author = {A. S. Fraenkel},
  year = 1974,
  title = {Combinatorial games with an annihilation rule},
  pages = {87-91},
  editor = {J. P. LaSalle},
  publisher = {Amer. Math. Soc., Providence, RI},
  volume = 20,
  booktitle = {The Influence of Computing on Mathematical Research and
Education, {\rm Missoula MT, August 1973}, \emph{Proc. Symp. Appl. Math.,}},
}

@article{Fra1977,
  author = {A. S. Fraenkel},
  year = 1977,
  title = {The particles and antiparticles game},
  journal = {Comput. Math. Appl.},
  volume = 3,
  pages = {327-328},
}

@article{Fra1980,
  author = {A. S. Fraenkel},
  year = 1980,
  title = {From Nim to Go},
  journal = {Ann. Discrete Math.},
  volume = 6,
  note = {Proc. Symp. on Combinatorial Mathematics, Combinatorial
Designs and Their Applications (J. Srivastava, ed.), Colorado State
Univ., Fort Collins, CO, June 1978},
  pages = {137-156},
}

@article{Fra1981,
  author = {A. S. Fraenkel},
  year = 1981,
  title = {Planar kernel and Grundy with $d\leq 3$, $d_{out}\leq 2$,
$d_{in}\leq 2$ are NP-complete},
  journal = {Discrete Appl. Math.},
  volume = 3,
  pages = {257-262},
}

@article{Fra1982,
  author = {A. S. Fraenkel},
  year = 1982,
  title = {How to beat your Wythoff games' opponent on three fronts},
  journal = {Amer. Math. Monthly},
  volume = 89,
  pages = {353-361},
}

@article{Fra1983,
  author = {A. S. Fraenkel},
  year = 1983,
  title = {15 Research problems on games},
  journal = {Discrete Math.},
  note = {in "Research Problems" section, Vols. {\bf 43-46}},
}

@article{Fra1984,
  author = {A. S. Fraenkel},
  year = 1984,
  title = {Wythoff games, continued fractions, cedar trees and Fibonacci searches},
  journal = {Theoret. Comput. Sci.},
  volume = 29,
  pages = {49-73},
  note = {an earlier version appeared in Proc. 10th Internat. Colloq.
on Automata, Languages and Programming (J. Diaz, ed.), Vol. 154,
Barcelona, July 1983, Lecture Notes in Computer Science,
Springer Verlag, Berlin, 1983, pp. 203--225},
}

@article{Fra1988,
  author = {A. S. Fraenkel},
  year = 1988,
  title = {The complexity of chess, Letter to the Editor},
  journal = {J. Recr. Math.},
  volume = 20,
  pages = {13-14},
}

@incollection{Fra1991,
  author = {A. S. Fraenkel},
  year = 1991,
  title = {Complexity of games},
  pages = {111-153},
  editor = {R. K. Guy},
  publisher = {Amer. Math. Soc., Providence, RI},
  volume = 43,
  booktitle = {Combinatorial Games, \emph{Proc. Symp. Appl. Math.}},
}

@article{Fra1994,
  author = {A. S. Fraenkel},
  year = 1994,
  title = {Even kernels},
  journal = {Electr. J. Combinatorics},
  volume = 1,
  pages = {\#R5, 13 pp.},
  url = {http://www.combinatorics.org/},
}

@article {MR1138949,
    AUTHOR = {Fraenkel, Aviezri S.},
     TITLE = {Iterated floor function, algebraic numbers, discrete chaos,
              {B}eatty subsequences, semigroups},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {341},
      YEAR = {1994},
     PAGES = {639--664},
      ISSN = {0002-9947},
     CODEN = {TAMTAM},
   MRCLASS = {11B83 (11B39 11Z50 58F13)},
  MRNUMBER = {MR1138949 (94d:11011)},
MRREVIEWER = {{\v{S}}tefan Porubsk{\'y}},
}

@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, 17 pp.},
  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 = {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)},
}

@article{Fra2002b,
  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 = {},
}

@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},
}

@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, 18 pp., 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{Fra2006,
  author = {A. S. Fraenkel},
  year = 2006,
  title = {Nim is easy, chess is hard --- but why??},
  journal = {J. Internat. Computer Games Assoc.},
  volume = {29},
  number = {4},
  pages = {203-206},
  note = {earlier version appeared in Plus Mag. {\rm
(}electronic{\rm )}, pluschat section,\hfill\break
http://plus.maths.org/issue40/editorial/index.html},
}

@inbook{Fra2007a,
  author = {A. S. Fraenkel},
  year = 2007,
  title = {The Raleigh game, {\rm in: Combinatorial Number Theory}},
  publisher = {de Gruyter},
  pages = {199-208},
  note = {Proc.\ Integers Conference, Carrollton, Georgia, October 27-30,2005,
in celebration of the 70th birthday of Ronald Graham. B.\ Landman,
M.\ Nathanson, J.\ Ne\v{s}et\v{r}il, R.\ Nowakowski, C. Pomerance eds.,
also appeared in {\it Integers, Electr.\ J.\ of Combinat.\ Number Theory\/} 
{\bf 7(2)}, special volume in honor of Ron Graham, \#A13, 11 pp.},
url = {http://www.integers-ejcnt.org/vol7(2).html},
MRNUMBER = {MR2337047 (2008e:91021)},
}

@article{Fra2007b,
  author = {A. S. Fraenkel},
  year = 2007,
  title = {Why are games exciting and stimulating?},
  journal = {Math Horizons},
  volume = {},
  pages = {5-7; 32-33},
  note = {special issue: ``Games, Gambling, and Magic" February. German
translation by Niek Neuwahl, poster-displayed at traveling exhibition
``Games \& Science, Science \& Games'', opened in G\"{o}ttingen
July 17 -- Aug 21, 2005},
}

@article{Fra2008a,
  author = {A. S. Fraenkel},
  year = 2008,
  title = {Games played by Boole and Galois},
  journal = {Discrete Appl. Math.},
  volume = {156},
  pages = {420-427},
  mrnumber = {**MR pending},
  }

@inbook{Fra2009,
  author = {A. S. Fraenkel},
  year = 2009,
  title = {The cyclic Butler University game, {\rm in: Mathematical 
  Wizardry for a Gardner, Volume honoring Martin Gardner}},
  pages = {},
  publisher = {A K Peters, Natick, MA},
  note = {E. Pegg Jr, A. H. Schoen, and T. Rodgers, eds., to appear},
}

@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},
}

@inbook{FrKo2007,
  author = {A. S. Fraenkel and A. Kontorovich},
  year = 2007,
  title = {The Sierpi\'{n}ski sieve of Nim-varieties and binomial
coefficients, {\rm in: Combinatorial Number Theory}},
  publisher = {de Gruyter},
  pages = {209-227},
  note = {Proc.\ Integers Conference, Carrollton, Georgia, October 27-30,2005,
in celebration of the 70th birthday of Ronald Graham. B.\ Landman,
M.\ Nathanson, J.\ Ne\v{s}et\v{r}il, R.\ Nowakowski, C. Pomerance eds.,
appeared also in {\it Integers, Electr.\ J.\ of Combinat.\ Number Theory\/} {\bf 7(2)},
special volume in honor of Ron Graham, \*A14, 19 pp.},
url = {http://www.integers-ejcnt.org/vol7(2).html},
MRNUMBER = {MR2337048},
}

@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},
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  note = {special issue: Creation and Recreation: A Tribute to the
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 BOOKTITLE = {6th Czech-Slovak International Symposium on Combinatorics,
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    SERIES = {Electron. Notes Discrete Math.},
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 PUBLISHER = {Elsevier},
   ADDRESS = {Amsterdam},
      YEAR = {2007},
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   MRCLASS = {05C20},
  MRNUMBER = {MR2233005},
}

@article {GaRi1998,
    AUTHOR = {Galeana-S{\'a}nchez, H. and Rinc{\'o}n-Mej{\'{\i}}a, H. A.},
     TITLE = {A sufficient condition for the existence of {$k$}-kernels in
              digraphs},
   JOURNAL = {Discuss. Math. Graph Theory},
  FJOURNAL = {Discussiones Mathematicae. Graph Theory},
    VOLUME = {18},
      YEAR = {1998},
     PAGES = {197--204},
      ISSN = {1234-3099},
   MRCLASS = {05C20},
  MRNUMBER = {MR1687843 (2000c:05074)},
MRREVIEWER = {Mat{\'u}{\v{s}} Harminc},
}

@article {GaRo2004,
    AUTHOR = {Galeana-S{\'a}nchez, Hortensia and Rojas-Monroy, Roc{\'{\i}}o},
     TITLE = {Kernels in pretransitive digraphs},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {275},
      YEAR = {2004},
     PAGES = {129--136},
      ISSN = {0012-365X},
     CODEN = {DSMHA4},
   MRCLASS = {05C20},
  MRNUMBER = {MR2026280 (2004j:05059)},
}

@article {MR2251578,
    AUTHOR = {Galeana-S{\'a}nchez, Hortensia and Rojas-Monroy, Roc{\'{\i}}o},
     TITLE = {Kernels in quasi-transitive digraphs},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {306},
      YEAR = {2006},
    NUMBER = {16},
     PAGES = {1969--1974},
      ISSN = {0012-365X},
     CODEN = {DSMHA4},
   MRCLASS = {05C20},
  MRNUMBER = {MR2251578 (2007b:05092)},
}

@article {MR2273872,
    AUTHOR = {Galeana-S{\'a}nchez, Hortensia and Rojas-Monroy, Roc{\'{\i}}o},
     TITLE = {Extensions and kernels in digraphs and in edge-coloured
              digraphs},
   JOURNAL = {WSEAS Trans. Math.},
  FJOURNAL = {WSEAS Transactions on Mathematics},
    VOLUME = {6},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {334--341},
      ISSN = {1109-2769},
   MRCLASS = {05C20 (05C15)},
  MRNUMBER = {MR2273872},
MRREVIEWER = {Mat{\'u}{\v{s}} Harminc},
}

@incollection {MR2279176,
    AUTHOR = {Galeana-S{\'a}nchez, Hortensia and Rojas-Monroy, Roc{\'{\i}}o},
     TITLE = {Kernels in orientations of pretransitive orientable graphs},
 BOOKTITLE = {Graph theory in Paris},
    SERIES = {Trends Math.},
     PAGES = {197--208},
 PUBLISHER = {Birkh\"auser},
   ADDRESS = {Basel},
      YEAR = {2007},
   MRCLASS = {05C20},
  MRNUMBER = {MR2279176},
}

@article {GGHR2006,
    AUTHOR = {Gallant, Robert P. and Gunther, Georg and Hartnell, Bert L.
              and Rall, Douglas F.},
     TITLE = {A game of edge removal on graphs},
   JOURNAL = {J. Combin. Math. Combin. Comput.},
  FJOURNAL = {Journal of Combinatorial Mathematics and Combinatorial
              Computing},
    VOLUME = {57},
      YEAR = {2006},
     PAGES = {75--82},
      ISSN = {0835-3026},
   MRCLASS = {05C99},
  MRNUMBER = {MR2226684 (2006m:05245)},
}

@article{Gal1978,
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  volume = 26,
  pages = {445-449},
}

@inproceedings{Gal1985,
  author = {F. Galvin},
  year = 1985,
  title = {Stationary strategies in topological games},
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  organization = {Publ. D\'ep. Math. Nouvelle S\'er. B, 85--2, Univ.
Claude-Bernard, Lyon},
  pages = {41-43},
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@incollection{Galv1990,
  author = {F. Galvin},
  year = 1990,
  title = {Hypergraph games and the chromatic number},
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  pages = {201-206},
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@article{GJM1978,
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  pages = {284-292},
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@article{GaSc1992,
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@article{GaTe1986,
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  pages = {51-69},
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@article{GaYel1995,
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  volume = 95,
  pages = {213-228},
}

@article{GaPl1989,
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  volume = 18,
  pages = {311-320},
}

@article{Gan1988,
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@book{Gar1956,
  author = {M. Gardner},
  year = 1956,
  title = {Mathematics, Magic and Mystery},
  publisher = {Dover, New York, NY},
}

@misc{Gar1957,
  author = {M. Gardner},
  year = {Jan. 1957--Dec. 1981},
  title = {Mathematical Games},
  note = {a column in Scientific American; all 15 volumes of the column are on 1 CD-ROM,
  available from MAA},
}

@book{Gar1959a,
  author = {M. Gardner},
  year = 1959,
  title = {Fads and Fallacies in the Name of Science},
  publisher = {Dover, NY},
}

@book{Gar1959b,
  author = {M. Gardner},
  year = 1959,
  title = {Logic Machines and Diagrams},
  publisher = {McGraw-Hill, NY},
}

@book{Gar1959c,
  author = {M. Gardner},
  year = 1959,
  title = {Mathematical Puzzles of Sam Loyd},
  publisher = {Dover, New York, NY},
}

@book{Gar1960,
  author = {M. Gardner},
  year = 1960,
  title = {More Mathematical Puzzles of Sam Loyd},
  publisher = {Dover, New York, NY},
}

@book{Gar1966,
  author = {M. Gardner},
  year = 1966,
  title = {More Mathematical Puzzles and Diversions},
  publisher = {Har\-monds\-worth, Middlesex, England (Penguin Books)},
  note = {translated into German: {\it Ma\-the\-matische R\"atsel und Probleme},
Vieweg, Braunschweig, 1964},
}

@book{Gar1967,
  editor = {M. Gardner},
  year = 1967,
  title = {536 Puzzles and Curious Problems},
  note = {reissue of H. E. Dudeney's {\it Modern Puzzles} and {\it Puzzles and
Curious Problems}},
  publisher = {Scribner's, NY},
}

@book{Gar1968,
  author = {M. Gardner},
  year = 1968,
  title = {Logic Machines, Diagrams and Boolean Algebra},
  publisher = {Dover, NY},
}

@book{Gar1970,
  author = {M. Gardner},
  year = 1970,
  title = {Further Mathematical Diversions},
  publisher = {Allen and Unwin, London},
}

@book{Gar1977,
  author = {M. Gardner},
  year = 1977,
  title = {Mathematical Magic Show},
  publisher = {Knopf, NY},
}

@book{Gar1978,
  author = {M. Gardner},
  year = 1978,
  title = {Aha! Insight},
  publisher = {Freeman, New York, NY},
}

@book{Gar1979,
  author = {M. Gardner},
  year = 1979,
  title = {Mathematical Circus},
  publisher = {Knopf, NY},
}

@book{Gar1981,
  author = {M. Gardner},
  year = 1981,
  title = {Entertaining Science Experiments with Everyday Objects},
  publisher = {Dover, NY},
}

@book{Gar1981a,
  author = {M. Gardner},
  year = 1981,
  title = {Science Fiction Puzzle Tales},
  publisher = {Potter},
}

@book{Gar1982,
  author = {M. Gardner},
  year = 1982,
  title = {Aha! Gotcha!},
  publisher = {Freeman, New York, NY},
}

@book{Gar1983,
  author = {M. Gardner},
  year = 1983,
  title = {New Mathematical Diversions from Scientific American},
  publisher = {University of Chicago Press, Chicago},
  note = {before that appeared in 1971, Simon and Schuster, New York, NY.
First appeared in 1966},
}

@book{Gar1983a,
  author = {M. Gardner},
  year = 1983,
  title = {Order and Surprise},
  publisher = {Prometheus Books, Buffalo, NY},
}

@book{Gar1983b,
  author = {M. Gardner},
  year = 1983,
  title = {Wheels, Life and Other Mathematical Amusements},
  publisher = {Freeman, New York, NY},
}

@book{Gar1984,
  author = {M. Gardner},
  year = 1984,
  title = {Codes, Ciphers and Secret Writing},
  publisher = {Dover, NY},
}

@book{Gar1984a,
  author = {M. Gardner},
  year = 1984,
  title = {Puzzles from Other Worlds},
  publisher = {Random House},
}

@book{Gar1984b,
  author = {M. Gardner},
  year = 1984,
  title = {The Magic Numbers of Dr. Matrix},
  publisher = {Prometheus},
}

@book{Gar1984c,
  author = {M. Gardner},
  year = 1984,
  title = {The Sixth Book of Mathematical Games},
  publisher = {Univ. of Chi\-ca\-go Press. First appeared in 1971, Freeman,
New York, NY},
}

@book{Gar1986,
  author = {M. Gardner},
  year = 1986,
  title = {Knotted Doughnuts and Other Mathematical Entertainments},
  publisher = {Freeman, New York, NY},
}

@book{Gar1987,
  author = {M. Gardner},
  year = 1987,
  title = {The Second Scientific American Book of Mathematical Puzzles and
Diversions},
  publisher = {University of Chicago Press, Chicago. First appeared in 1961,
Simon and Schuster, NY},
}

@book{Gar1988,
  author = {M. Gardner},
  year = 1988,
  title = {Hexaflexagons and Other Mathematical Diversions},
  publisher = {University of Chicago Press, Chicago, 1988. A first version
appeared under the title {\it The Scientific American Book of Mathematical
Puzzles and Diversions}, Simon \& Schuster, 1959, NY},
}

@book{Gar1988a,
  author = {M. Gardner},
  year = 1988,
  title = {Perplexing Puzzles and Tantalizing Teasers},
  publisher = {Dover, NY},
}

@book{Gar1988b,
  author = {M. Gardner},
  year = 1988,
  title = {Riddles of the Sphinx},
  publisher = {Math. Assoc. of America, Washington, DC},
}

@book{Gar1988c,
  author = {M. Gardner},
  year = 1988,
  title = {Time Travel and Other Mathematical Bewilderments},
  publisher = {Freeman, New York, NY},
}

@book{Gar1989,
  author = {M. Gardner},
  year = 1989,
  title = {How Not to Test a Psychic},
  publisher = {Prometheus Books, Buffalo, NY},
}

@book{Gar1989a,
  author = {M. Gardner},
  year = 1989,
  title = {Mathematical Carnival},
  publisher = {2nd edition, Math. Assoc. of America, Washington, DC.
First appeared in 1975, Knopf, NY},
}

@book{Gar1990,
  author = {M. Gardner},
  year = 1990,
  title = {The New Ambidextrous Universe},
  publisher = {Freeman, New York, NY. First appeared in 1964, Basic Books,
then in 1969, New American Library},
}

@book{Gar1991,
  author = {M. Gardner},
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  title = {The Unexpected Hanging and Other Mathematical Diversions},
  publisher = {University of Chicago Press. First appeared in 1969, Simon
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  note = {adapted from ``Further Mathematical Diversions"; translated into German:
  {\it Logik Unterm Galgen}, Vieweg, Braunschweig, 1980},
}

@book{Gar1992,
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  publisher = {Freeman, New York, NY},
}

@book{Gar1992a,
  author = {M. Gardner},
  year = 1992,
  title = {On the Wild Side},
  publisher = {Prometheus Books, Buffalo, NY},
}

@book{Gar1993,
  author = {M. Gardner},
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  publisher = {Dover, NY},
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@book{Gar1997,
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  publisher = {The Math. Assoc. of America, Washington, DC. First
appeared in 1989, Freeman, New York, NY. Freeman, New York, NY},
}

@book{Gar1997a,
  author = {M. Gardner},
  year = 1997,
  title = {The Last Recreations},
  publisher = {Copernicus, NY},
}

@book{Gar2001,
  author = {M. Gardner},
  year = 2001,
  title = {A Gardner's Workout: Training the Mind and Entertaining the Spirit},
  publisher = {A K Peters, Natick, MA},
}

@book{GaJo1979,
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  year = 1979,
  publisher = {Freeman, San Francisco},
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              {M}athematical {C}onference ({S}ingapore, 1979), {V}ol.\ {II}},
   JOURNAL = {Rend. Accad. Sci. Fis. Mat. Napoli (4)},
  FJOURNAL = {Societ\`a Nazionale di Scienze, Lettere ed Arti in Napoli.
              Rendiconto dell'Accademia delle Scienze Fisiche e Matematiche.
              Serie IV},
    VOLUME = 46,
      YEAR = 1979,
     PAGES = {259--263 (1980)},
      ISSN = {0370-3568},
     CODEN = {RASFAM},
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  MRNUMBER = {MR582263 (83c:05103)},
}
		
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INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 8 (2008), #A45
UNIVERSAL SETS AND THE VECTOR GAME
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  year = 1993,
  title = {The memory game},
  journal = {Theoret. Comput. Sci. \emph{(Math Games)}},
  volume = 110,
  pages = {169-196},
}

@article{ZwPa1996,
  author = {U. Zwick and M. S. Paterson},
  year = 1996,
  title = {The complexity of mean payoff games on graphs},
  journal = {Theoret. Comput. Sci. \emph{(Math Games)}},
  volume = 158,
  pages = {343-359},
}

@article{Zwi1987,
  author = {W. S. Zwicker},
  year = 1987,
  title = {Playing games with games: the hypergame paradox},
  journal = {Amer. Math. Monthly},
  volume = 94,
  pages = {507-514},
}