Entire coloring of plane graph with maximum degree eleven

A plane graph is called entirely k -colorable if for each x ∈ V ( G ) ∪ E ( G ) ∪ F ( G ) , we can use k colors to assign each element x a color such that any two elements that are adjacent or incident receive distinct colors. In this paper, we prove that if G is a plane graph with Δ = 11 , then G is entirely ( Δ + 2 ) -colorable, which provides a positive answer to a problem posed by Borodin (Problem 5.2 in Borodin (2013)).