Entire coloring of plane graph with maximum degree eleven

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