... with game chromatic number The question whether there exist outerplanar graphs with game chromatic number or not is still an open question We shall prove in this section that the oriented game chromatic ... have bounded (oriented or not) game chromatic number Using that, we prove in Section that the families of oriented paths, oriented cycles or oriented trees have bounded oriented game chromatic number ... oriented path or an oriented cycle, then ogcn(G) ≤ In fact, this bound is tight, as shown by the following: Theorem There exist oriented paths with oriented game chromatic number Proof The idea is to...