Plane graphs with maximum degree 9 are entirely 11-choosable

A plane graph G is entirely k -choosable if, for every list L of colors satisfying L ( x ) = k for all x ź V ( G ) ź E ( G ) ź 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 ź 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.

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