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On the complexity of some coloring games

  • Hans L. Bodlaender
Graph Algorithms And Complexity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 484)

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 never two adjacent vertices are 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 to determine whether there is a winning strategy for player 1 is PSPACE-complete for any C with |C| ≥ 3, but the problems are solvable in O(n + eα(e, n)), and O(n + e) 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.

Keywords

Polynomial Time Algorithm Chromatic Number Conjunctive Normal Form Outgoing Edge Linear Time Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Hans L. Bodlaender
    • 1
  1. 1.Department of Computer ScienceUtrecht UniversityUtrechtthe Netherlands

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