Affiliation:
1. Department of Computer Science, Utrecht University, P.O. Box 80.089, 3508 TB Utrecht, the Netherlands
Abstract
In this paper we consider the following game: players must alternately color the lowest numbered uncolored vertex of a given graph G= ({1, 2,…, n}, E) with a color, taken from a given set C, such that two adjacent vertices are never colored with the same color. In one variant, the first player which is unable to move, loses the game. In another variant, player 1 wins the game if and only if the game ends with all vertices colored. We show that for both variants, the problem of determining whether there is a winning strategy for player 1 is PSPACE-complete for any C with |C|≥3, but the problems are solvable in [Formula: see text], and [Formula: see text] time, respectively, if |C|=2. We also give polynomial time algorithms for the problems with certain restrictions on the graphs and orderings of the vertices. We give some partial results for the versions where no order for coloring the vertices is specified.
Publisher
World Scientific Pub Co Pte Lt
Subject
Computer Science (miscellaneous)
Cited by
105 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献