乘积图的博弈染色数
The Game Coloring Number of Product Graph
DOI: 10.12677/AAM.2023.124156, PDF, HTML, 下载: 153  浏览: 228 
作者: 苏俊义：浙江师范大学数学科学学院，浙江 金华
关键词: 笛卡尔积图；直积图；强积图；博弈染色数；The Cartesian Product of Graphs； The Direct Product of Graphs； The Strong Product of Graphs； Game Coloring Number
摘要: 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.
Abstract: 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.
文章引用：苏俊义. 乘积图的博弈染色数[J]. 应用数学进展, 2023, 12(4): 1504-1509. https://doi.org/10.12677/AAM.2023.124156

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