A note on entire choosability of plane graphs

AbstractA plane graph is called entirely k-choosable if for any list assignment L such that ∣L(x)∣=k for each x∈V(G)∪E(G)∪F(G), we can assign each element x a color from its list such that any two elements that are adjacent or incident receive distinct colors. Wang and Lih (2008) [5] conjectured that every plane graph is entirely (Δ+4)-choosable and showed that the conjecture is true if Δ≥12. In this note, we prove that (1) Every plane graph G with Δ≥7 is entirely (Δ+4)-choosable. (2) Every plane graph G with Δ≥6 is entirely (Δ+5)-choosable