θ-图的对策着色和对策色数

The Game Coloring and Chromatic Number of θ-Graph

介绍了一种新的二人对策着色:色对策Ⅱ和对策色数Ⅱ.比较了两种色对策的差异,讨论了图G的色对策Ⅱ的性质.在路图和图圈的基础上,利用顶点标号的方法,分别对θ-图和广义θ-图分情况进行了讨论,并得出了它们的对策色数Ⅱ.给出了二人对策着色中使选手A获胜的策略,并推广了此结论.得出了均匀θ-图的对策色数Ⅱ,给出了二人对策着色中选手A的获胜策略.

First, this paper introduces a new two-person game coloring, game chromatic and game chromatic number. Their difference is compared, and the properties of the game chromatic number Ⅱ are discussed. Second, on the basis of the path and cycle, the game chromatic numbers of θ-graph and general θ-graph are obtained respectively, and the winning strategy for A player is presented. Finally, the results are extended to obtain the game chromatic number of even θ-graph, and the winning strategy for A player is given.