Plane Graphs with Maximum Degree 6 are Edge-face 8-colorable.

A plane graph G is edge-face k-colorable if the elements of $${E(G) \cup F(G)}$$ can be colored with k colors so that any two adjacent or incident elements receive different colors. Sanders and Zhao conjectured that every plane graph with maximum degree Δ is edge-face (Δ + 2)-colorable and left the cases $${\Delta \in \{4, 5, 6\}}$$ unsolved. In this paper, we settle the case Δ = 6. More precisely, we prove that every plane graph with maximum degree 6 is edge-face 8-colorable. [ABSTRACT FROM AUTHOR]