Plane graphs with maximum degree 9 are entirely 11-choosable

A plane graph GG is entirely kk-choosable if, for every list LL of colors satisfying L(x)=kL(x)=k for all x∈V(G)∪E(G)∪F(G)x∈V(G)∪E(G)∪F(G), there exists a coloring which assigns to each vertex, each edge and each face a color from its list so that any adjacent or incident elements receive different colors. It was known that every plane graph GG with maximum degree Δ≥10Δ≥10 is entirely (Δ+2)(Δ+2)-choosable. In this paper, we improve this result by showing that every plane graph GG with Δ=9Δ=9 is entirely 11-choosable.