On the oriented game chromatic number

Abstract

We consider the oriented version of a coloring game introduced by Bodlaender [On the complexity of some coloring games, Internat. J. Found. Comput. Sci. 2 (1991), 133-147]. We prove that every oriented path has oriented game chromatic number at most 7 (and this bound is tight), that every oriented tree has oriented game chromatic number at most 19 and that there exists a constant t such that every oriented outerplanar graph has oriented game chromatic number at most t.