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

A plane graph G is said to be edge-face k -choosable if, for every list L of colors satisfying | L ( x ) | = k for 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 G with maximum degree Δ ( G ) ≥ 9 is edge-face ( Δ ( G ) + 1 ) -choosable.