树和路的乘积图的广义染色数及博弈染色数

The Generalized Coloring Number and Game Coloring Number of Product Graph of Treeand Path

摘要: 本文讨论了简单图树和路的乘积图，给出了树和路的乘积图的一个线性序，介绍了它的广义染色数，同时给出了树和路的乘积图最大出度限制为一个常数的一个定向，并由此介绍了树和路的乘积图的博弈染色数。

Abstract: This paper considers the product graph of simple graph tree and path, gives a linear order of the product graph of tree and path, and introduces the generalized coloring number of the product graph of tree and path. Meanwhile, we give an orientation that the maximum out-degree of the product graph of tree and path is at most a constant and introduce the game coloring number of the product graph of tree and path.