PLANE GRAPHS ARE ENTIRELY (Δ + 5)-CHOOSABLE
Xiaoxue Hu, Yiqiao Wang · Discrete Mathematics Algorithms and Applications · 2014
A plane graph G is entirely k-choosable if, for every list L of colors satisfying L(x) = k for 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. In this paper, we show that every plane graph G with maximum degree Δ ≤ 5 is entirely (Δ + 5)-choosable.