乘积图的博弈染色数

The Game Coloring Number of Product Graph

本文讨论的图是两棵树的乘积图. 分别研究了树和树的笛卡尔积图、直积图和强积图的 (a, 1)-博弈染色数, 给出了三种乘积图的 (a, 1)-博弈染色的上界. 特殊地, 如果其中一棵树是一条路, 那么我们类似的可以得出关于树和路的乘积图的 (a, 1)-博弈染色数的结果.

The graph discussed in this article is a product graph of two trees. We study the (a, 1)-game coloring numbers of the Cartesian product graph, direct product graph and strong product graphs of two trees, and give the upper bounds of (a, 1)-game coloring numbers of the three product graphs. In particular, if one of the trees is a path, then we can similarly obtain the results of the (a, 1)-game coloring number of the product graph of tree and path.