Edge-face coloring of plane graphs with maximum degree nine

摘要

An edge-face coloring of a plane graph with edge set E and face set F is a coloring of the elements of E∪F so that adjacent or incident elements receive different colors. Borodin [Discrete Math 128(1-3):21-33, 1994] proved that every plane graph of maximum degree δ≥10 can be edge-face colored with δ + 1 colors. We extend Borodin's result to the case where δ = 9.