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Chomp on generalized Kneser graphs and others

Author

Listed:
  • Ignacio García-Marco

    (Universidad de La Laguna)

  • Kolja Knauer

    (Université de Toulon, CNRS, LIS)

  • Luis Pedro Montejano

    (CONACYT Research Fellow—Centro de Investigación en Matemáticas)

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.

Suggested Citation

  • Ignacio García-Marco & Kolja Knauer & Luis Pedro Montejano, 2021. "Chomp on generalized Kneser graphs and others," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(3), pages 603-621, September.
    • Handle: RePEc:spr:jogath:v:50:y:2021:i:3:d:10.1007_s00182-019-00697-x
    DOI: 10.1007/s00182-019-00697-x
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    References listed on IDEAS

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    1. Schwalbe, Ulrich & Walker, Paul, 2001. "Zermelo and the Early History of Game Theory," Games and Economic Behavior, Elsevier, vol. 34(1), pages 123-137, January.
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