Game coloring the Cartesian product of graphs

@article{Zhu2008GameCT,
  title={Game coloring the Cartesian product of graphs},
  author={Xuding Zhu},
  journal={Journal of Graph Theory},
  year={2008},
  volume={59},
  pages={261-278}
}
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… CONTINUE READING
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