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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 χ g (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)
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.