The game coloring number of planar graphs with a given girth.

Abstract: This paper discusses the game coloring number of planar graphs. Let be a planar graph and let be the game coloring number of . We prove that is at most 13 if is a planar graph with girth at least 4. We also show that there is a planar graph with girth 4 such that and there is a planar graph with girth 5 such that . [Copyright &y& Elsevier]