The Game Chromatic Number of Complete Multipartite Graphs with No Singletons

04/24/2023

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by   Paweł Obszarski, et al.

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In this paper we investigate the game chromatic number for complete multipartite graphs. We devise several strategies for Alice, and one strategy for Bob, and we prove their optimality in all complete multipartite graphs with no singletons. All the strategies presented are computable in linear time, and the values of the game chromatic number depend directly only on the number and the sizes of sets in the partition.