B. Liu, L. Sun , B. Wang, J.-L. Wu
The list coloring and list total coloring of planar graphs with maximum degree at least 7
Discussiones Mathematicae Graph Theory
Received 13.02.2017, Revised 02.06.2018, Accepted 21.06.2018, doi: 10.7151/dmgt.2160

A graph G is edge k-choosable (respectively, total k-choosable) if, whenever we are given a list L(x) of colors with |L(x)|=k for each x∈E(G) (x∈E(G)∪ V(G)), we can choose a color from L(x) for each element x such that no two adjacent (or incident) elements receive the same color. The list edge chromatic index χ'l(G) (respectively, the list total chromatic number χ''l(G)) of G is the smallest integer k such that G is edge (respectively, total) k-choosable. In this paper, we focus on a planar graph G, with maximum degree Δ(G)≥ 7 and with some structural restrictions, satisfies χ'l(G)=Δ(G) and χ''l(G)=Δ(G)+1.
planar graph, list edge coloring, list total coloring