Every planar graph with Δ ${\rm{\Delta }}$ ⩾ 8 is totally (Δ+2) $({\rm{\Delta }}+2)$‐choosable
Marthe Bonamy, Théo Pierron, Éric Sopena · Journal of Graph Theory · 2023
Abstract Total 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.