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 col g ( G ) be the game coloring number of G . We prove that col g ( 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 col g ( G ) ≥ 7 and there is a planar graph with girth 5 such that col g ( G ) ≥ 6 .