The edge-face choosability of plane graphs with maximum degree at least 9

A plane graph GG is said to be edge-face kk-choosable if, for every list LL of colors satisfying |L(x)|=k|L(x)|=k for x∈E(G)∪F(G)x∈E(G)∪F(G), there exists a coloring which assigns to each edge and face a color from its list so that any adjacent or incident elements receive different colors. In this paper, we prove that every plane graph GG with maximum degree Δ(G)≥9Δ(G)≥9 is edge-face (Δ(G)+1)(Δ(G)+1)-choosable.