Every planar graph with Δ ${\rm{\Delta }}$ ⩾ 8 is totally (Δ+2) $({\rm{\Delta }}+2)$‐choosable

Abstract

AbstractTotal coloring is a variant of edge coloring where both vertices and edges are to be colored. A graph is totally ‐choosable if for any list assignment of colors to each vertex and each edge, we can extract a proper total coloring. In this setting, a graph of maximum degree needs at least colors. In the planar case, Borodin proved in 1989 that colors suffice when is at least 9. We show that this bound also holds when is 8.