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The Complexity of Graph Ramsey Games

Part of the Lecture Notes in Computer Science book series (LNCS,volume 2063)

Abstract

We consider combinatorial avoidance and achievement games based on graph Ramsey theory: The players take turns in coloring edges of a graph G, each player being assigned a distinct color and choosing one so far uncolored edge per move. In avoidance games, completing a monochromatic subgraph isomorphic to another graph A leads to immediate defeat or is forbidden and the first player that cannot move loses. In the avoidance+ variant, both players are free to choose more than one edge per move. In achievement games, the first player that completes a monochromatic subgraph isomorphic to A wins. We prove that general graph Ramsey avoidance, avoidance+, and achievement endgames and several variants thereof are PSPACE-complete.

Keywords

  • combinatorial games
  • graph Ramsey theory
  • Ramsey game
  • PSPACE-completeness
  • complexity
  • edge coloring
  • winning strategy
  • achievement game
  • avoidance game
  • the game of Sim
  • Java applet
  • endgames

Acknowledgments

This research was partially supported by Austrian Science Fund Project N Z29-INF. I am grateful to the anonymous reviewers for their valuable comments.

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Slany, W. (2001). The Complexity of Graph Ramsey Games. In: Marsland, T., Frank, I. (eds) Computers and Games. CG 2000. Lecture Notes in Computer Science, vol 2063. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45579-5_12

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  • DOI: https://doi.org/10.1007/3-540-45579-5_12

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