Strong edge-coloring of planar graphs
Lianying Miao, Wenyao Song · Discussiones Mathematicae Graph Theory · 2017
A strong edge-coloring of a graph is a proper edge-coloring where each color class induces a matching. We denote by s (G) the strong chromatic index of G which is the smallest integer k such that G can be strongly edgecolored with k colors. It is known that every planar graph G has a strong edge-coloring with at most 4(G) + 4 colors [R.J. Faudree, A. Gyrfs, R.H. Schelp and Zs. Tuza, The strong chromatic index of graphs, Ars Combin. 29B (1990) 205-211]. In this paper, we show that if G is a planar graph with g 5, then s (G) 4(G) -2 when (G) 6 and s (G) 19 when (G) = 5, where g is the girth of G.