Star 5-edge-colorings of subcubic multigraphs

The star chromatic index of a mulitigraph G, denoted chi(s)'(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 chi(s)'(G) <= k. Dvorak et al. (2013) proved that every subcubic multigraph is star 7-edge-colorable, and conjectured that every subcubic multigraph should be star 6-edge-colorable. Kerdjoudj, Kostochka and Raspaud considered the list version of this problem for simple graphs and proved that every subcubic graph with maximum average degree less than 7/3 is star list-5-edge-colorable. It is known that a graph with maximum average degree 14/5 is not necessarily star 5-edge-colorable. In this paper, we prove that every subcubic multigraph with maximum average degree less than 12/5 is star 5-edge-colorable. (C) 2017 Elsevier B.V. All rights reserved.