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Chomp on generalized Kneser graphs and others

  • Ignacio García-Marco
  • Kolja Knauer
  • Luis Pedro MontejanoEmail author
Original Paper
  • 20 Downloads

Abstract

In Chomp on graphs, two players alternatingly pick an edge or a vertex from a graph. The player that cannot move any more loses. The questions one wants to answer for a given graph are: Which player has a winning strategy? Can an explicit strategy be devised? We answer these questions (and determine the Nim-value) for the class of generalized Kneser graphs and for several families of Johnson graphs. We also generalize some of these results to the clique complexes of these graphs. Furthermore, we determine which player has a winning strategy for some classes of threshold graphs.

Keywords

Combinatorial games Impartial games Chomp Generalized Kneser graphs Johnson graphs Threshold graphs Clique complex 

Mathematics Subject Classification

05C57 91A05 91A46 91A43 91A05 

Notes

Acknowledgements

Both I.G. and K.K. thank L.P.M. and Mireia Ferrer for their hospitality and the good time spent during the stay in Guanajuato. We thank Cormac O’Sullivan for pointing out an error in a theorem about almost bipartite graphs stated in an earlier version of the paper.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Facultad de CienciasUniversidad de La LagunaLa LagunaSpain
  2. 2.Aix Marseille UnivUniversité de Toulon, CNRS, LISMarseilleFrance
  3. 3.CONACYT Research Fellow—Centro de Investigación en MatemáticasGuanajuatoMexico

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