The incidence game chromatic number

Abstract

We introduce the incidence game chromatic number which unifies the ideas of game chromatic number and incidence coloring number of an undirected graph. For k-degenerate graphs with maximum degree @D, the upper bound 2@D+4k-2 for the incidence game chromatic number is given. If @D>=5k, we improve this bound to the value 2@D+3k-1. We also determine the exact incidence game chromatic number of cycles, stars and sufficiently large wheels and obtain the lower bound 32@D for the incidence game chromatic number of graphs of maximum degree @D.