Geodesic
List Star Edge-Coloring of Subcubic Graphs
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 4, pp. 1037-1054

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A star edge-coloring of a graph G is a proper edge coloring such that every 2-colored connected subgraph of G is a path of length at most 3. For a graph G, let the list star chromatic index of G, ch_st^' (G), be the minimum k such that for any k-uniform list assignment L for the set of edges, G has a star edge-coloring from L. Dvořák, Mohar and Šámal asked whether the list star chromatic index of every subcubic graph is at most 7. We prove that it is at most 8. We also prove that if the maximum average degree of a subcubic graph G is less than 73 (respectively, 52), then ch_st^' (G) ≤ 5 (respectively, ch_st^' (G) ≤ 6).
Keywords: graph coloring, edge coloring, star coloring, planar graphs 
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     title = {List {Star} {Edge-Coloring} of {Subcubic} {Graphs}},
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Kerdjoudj, Samia; Kostochka, Alexandr; Raspaud, André. List Star Edge-Coloring of Subcubic Graphs. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 4, pp. 1037-1054. http://geodesic.mathdoc.fr/item/DMGT_2018_38_4_a11/