Geodesic
The List Edge Coloring and List Total Coloring of Planar Graphs with Maximum Degree at Least 7
Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 4, pp. 1005-1024

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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.
Keywords: planar graph, list edge coloring, list total coloring 
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     author = {Sun, Lin and Wu, Jianliang and Wang, Bing and Liu, Bin},
     title = {The {List} {Edge} {Coloring} and {List} {Total} {Coloring} of {Planar} {Graphs} with {Maximum} {Degree} at {Least} 7},
     journal = {Discussiones Mathematicae. Graph Theory},
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Sun, Lin; Wu, Jianliang; Wang, Bing; Liu, Bin. The List Edge Coloring and List Total Coloring of Planar Graphs with Maximum Degree at Least 7. Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 4, pp. 1005-1024. http://geodesic.mathdoc.fr/item/DMGT_2020_40_4_a4/