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- Tomasz Bartnicki, Bostjan Bresar, Jaroslaw Grytczuk, Matjaz Kovse, Zofia Miechowicz, Iztok Peterin
- Electr. J. Comb.
- 2007

The game chromatic number χg is considered for the Cartesian product G 2 H of two graphs G and H. We determine exact values of χg(G2H) when G and H belong to certain classes of graphs, and 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… (More)

- Tomasz Bartnicki, Zofia Miechowicz
- ArXiv
- 2012

Total variant of well known graph coloring game is considered. We determine exact values of χ′′ g for some classes of graphs and show that total game chromatic number is bounded from above by ∆ + 3∆. We also show relation between total game coloring number and game coloring index.

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