Game Chromatic Number of Cartesian Product Graphs

@article{Bartnicki2007GameCN,
  title={Game Chromatic Number of Cartesian Product Graphs},
  author={Tomasz Bartnicki and Bostjan Bresar and Jaroslaw Grytczuk and Matjaz Kovse and Zofia Miechowicz and Iztok Peterin},
  journal={Electr. J. Comb.},
  year={2007},
  volume={15}
}
The game chromatic number χg is considered for the Cartesian product G2H of two graphs G and H and exact values of χg(G2H) are determined when G and H belong to certain classes of graphs. By using a newly introduced ”game of combinations” we show that, in general, the game chromatic number χg(G2H) is not bounded from above by a function of game chromatic numbers of graphs G and H. An analogous result is proved for the game coloring number colg(G2H) of the Cartesian product of graphs. 

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