On strong edge-coloring of graphs with maximum degree 4

摘要

The strong chromatic index of a graph G, denoted by chi(s)'(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 Delta(G) = 4 and maximum average degree less than 61/18 (res.7/2, 18/5, 15/4, 51/13), then chi(s)'(G) = 16 (resp.17, 18, 19, 20), which improves the results of Bensmail et al. (2015). (C) 2017 Elsevier B.V. All rights reserved.