On strong edge-coloring of graphs with maximum degree 4

The strong chromatic index of a graph G, denoted by χs′(G), is the least number of colors needed to edge-color G properly so that every path of length 3 uses three different colors. In this paper, we prove that if G is a graph with Δ(G)=4 and maximum average degree less than 6118 (resp.72, 185, 154, 5113), then χs′(G)≤16 (resp.17, 18, 19, 20), which improves the results of Bensmail et al. (2015).