Game coloring the Cartesian product of graphs

: This article proves the following result: Let G and G be graphs of orders n and n , respectively. Let G be obtained from G by adding to each vertex a set of n degree 1 neighbors. If G has game coloring number m and G has acyclic chromatic number k, then the Cartesian product G G has game chromatic number at most k(k+m - 1). As a consequence, the Cartesian product of two forests has game chromatic number at most 10, and the Cartesian product of two planar graphs has game chromatic number at most 105.

• Type: Journal
• Year: 2008
• Where: JGT
• Authors: Xuding Zhu
• Keywords: Cartesian Product, Chromatic Number, Game, JGT 2008