Game chromatic number of some convex polytope graphs

Abstract

The game chromatic number Xg is considered for some convex polytope graphs. We find the exact values for the game chromatic number of Cartesian product graph P₃ □ P_n and P₃ □ C_n. This extends previous results of Bartnicki et al [3] and Sia [12] on the game chromatic number of Cartesian product graphs. We have also determined the exact value for the game chromatic number of an infinite convex polytope graph T_n [9].