Abstract
Node Kayles is a well-known two-player impartial game on graphs: Given an undirected graph, each player alternately chooses a vertex not adjacent to previously chosen vertices, and a player who cannot choose a new vertex loses the game. The problem of deciding if the first player has a winning strategy in this game is known to be PSPACE-complete. A few researches on algorithmic aspects of Node Kayles have been done so far. In this paper, we consider the problem from the view point of fixed-parameter tractability. We show that the problem is fixed-parameter tractable parameterized by the size of a minimum vertex cover or the modular-width of the given graph.
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Acknowledgments
The author thanks Kensuke Kojima for simplifying the proof of Lemma 5 and anonymous reviewers for valuable comments. This work was partially supported by JST CREST JPMJCR1401.
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Kobayashi, Y. (2021). On Structural Parameterizations of Node Kayles. In: Akiyama, J., Marcelo, R.M., Ruiz, MJ.P., Uno, Y. (eds) Discrete and Computational Geometry, Graphs, and Games. JCDCGGG 2018. Lecture Notes in Computer Science(), vol 13034. Springer, Cham. https://doi.org/10.1007/978-3-030-90048-9_8
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DOI: https://doi.org/10.1007/978-3-030-90048-9_8
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