Plane graphs with $$\Delta =7$$Δ=7 are entirely 10-colorable

A plane graph G is entirely k-colorable if $$V(G)\cup E(G) \cup F(G)$$ can be colored with k colors such that any two adjacent or incident elements receive different colors. In 2011, Wang and Zhu conjectured that every plane graph G with maximum degree $$\Delta \ge 3$$ and $$G\ne K_4$$ is entirely $$(\Delta +3)$$-colorable. It is known that the conjecture holds for the case $$\Delta \ge 8$$. The condition $$\Delta \ge 8$$ is improved to $$\Delta \ge 7$$ in this paper.