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# 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} }

- Published 2008 in Journal of Graph Theory
DOI:10.1002/jgt.20338

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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