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On the Complexity of Some Map-Coloring Multi-player Games

  • Alessandro CincottiEmail author
Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 52)

Abstract

Col and Snort are two-player map-coloring games invented respectively by Colin Vout and Simon Norton where to establish who has a winning strategy on a general graph is a \(\mathcal{P}SPACE\)-complete problem. However, winning strategies can be found on specific graph instances, e.g., strings or trees. In multi-player games, because of the possibility to form alliances, cooperation between players is a key-factor to determine the winning coalition and, as a result, the complexity of three-player Col played on trees is \(\mathcal{N}\mathcal{P}\)-complete and the complexity of n-player Snort played on bipartite graphs is \(\mathcal{P}\mathcal{S}\mathcal{P}\mathcal{A}\mathcal{C}\mathcal{E}\)-complete.

Keywords

Complexity Map-coloring game Multi-player game 

Notes

Acknowledgments

The author wishes to thank Mark G. Elwell for a careful reading of the manuscript.

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.School of Information ScienceJapan Advanced Institute of Science and TechnologyNomiJapan

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