“…This problem has also been studied for restricted classes of graphs, including: bipartite graphs [15,16], C 4 -free graphs [25], random graphs [17], graphs of bounded degeneracy [4,7,11], planar graphs [16,22,24], unit distance graphs [10] and graphs of maximum degree 3 and 4 [1,9,[19][20][21]. In particular, the strong chromatic index of a claw-free graph with maximum degree D is at most 1:125D 2 þ D [12].…”