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.

翻译：本文研究完全多部图的博弈色数。我们设计了若干针对Alice的策略及一个针对Bob的策略，并证明了它们在所有不含孤立顶点集的完全多部图中具有最优性。所提出的所有策略均可在线性时间内计算，且博弈色数的值仅直接依赖于划分中集合的数量及其基数。