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Kayles on Special Classes of Graphs -- An application of Sprague-Grundy theory

By Hans L. Bodlaender

Abstract

Kayles is the game, where two players alternately choose a vertex that has not been chosen before nor is adjacent to an already chosen vertex from a given graph. The last player that choses a vertex wins the game. We show, with help of Sprague-Grundy theory, that the problem to determine which player has a winning strategy for a given graph, can be solved in O(n³) time on interval graphs, on circular arc graphs, on permutation graphs, and on co-comparability graphs and in O(n^1.631) time on cographs. For general graphs, the problem is known to be PSPACE-complete, but can be solved in time polynomial in the number of isolatable sets of vertices of the graph

Publisher: Springer Verlag
Year: 1993
OAI identifier: oai:CiteSeerX.psu:10.1.1.19.4793
Provided by: CiteSeerX
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