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The edge-face chromatic number χ e f (G) of a plane graph G is the least number of colors such that any two adjacent or incident elements in E (G) ∪ F (G) receive different colors. In 2005, Luo and Zhang proved that each 2-connected simple graph G with Δ ≥ 24 has χ e f (G) = Δ. The condition Δ ⩾ 24 is improved to Δ ⩾ 13 in this paper. [ABSTRACT FROM AUTHOR]

A plane graph G is edge‐face k‐colorable if its edges and faces can be colored with k colors such that any two adjacent or incident elements receive different colors. It is known that every plane graph G of maximum degree Δ ≥ 8 is edge‐face (Δ + 1)‐colorable. The condition Δ ≥ 8 is improved to Δ ≥ 7 in this paper. [ABSTRACT FROM AUTHOR]

A plane graph G is entirely k -choosable if, for every list L of colors satisfying L ( x ) = k for all 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 G with maximum degree Δ ≥ 10 is entirely ( Δ + 2 ) -choosable. In this paper, we improve this result by showing that every plane graph G with Δ = 9 is entirely 11-choosable. [ABSTRACT FROM AUTHOR]

Abstract: A plane graph is said to be edge-face -choosable if, for every list of colors satisfying for , 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 with maximum degree is edge-face -choosable. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]