An upper bound for the choice number of star edge coloring of graphs

摘要

The star chromatic index of a multigraph G, denoted χs′(G), is the minimum number of colors needed to properly color the edges of G such that no path or cycle of length four is bi-colored. A multigraph G is star k-edge-colorable if χs′(G)≤k. Dvořák et al. (2013) proved that every subcubic multigraph is star 7-edge-colorable. They conjectured in the same paper that every subcubic multigraph should be star 6-edge-colorable. In this paper, we consider this problem in a more general setting, we investigate star list edge coloring of general graph G and obtain an upper bound for the choice number of star edge coloring of graphs, namely, we proved that χsl′≤⌈2Δ32(1Δ+2)12+2Δ⌉.