The game coloring number of planar graphs with a given girth

This paper discusses the game coloring number of planar graphs. Let G be a planar graph and let colg(G) be the game coloring number of G. We prove that colg(G) is at most 13 if G is a planar graph with girth at least 4. We also show that there is a planar graph G with girth 4 such that colg(G)≥7 and there is a planar graph with girth 5 such that colg(G)≥6.