Geodesic
Strong Edge-Coloring Of Planar Graphs
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 4, pp. 845-857

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A strong edge-coloring of a graph is a proper edge-coloring where each color class induces a matching. We denote by χ_s^' (G) the strong chromatic index of G which is the smallest integer k such that G can be strongly edge-colored with k colors. It is known that every planar graph G has a strong edge-coloring with at most 4 Δ (G) + 4 colors [R.J. Faudree, A. Gyárfás, 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 χ_s^' (G) ≤ 4 Δ (G) − 2 when Δ (G) ≥ 6 and χ_s^' (G) ≤ 19 when Δ (G) = 5, where g is the girth of G.
Keywords: strong edge-coloring, strong chromatic index, planar graph, dis- charging method 
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Song, Wen-Yao; Miao, Lian-Ying. Strong Edge-Coloring Of Planar Graphs. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 4, pp. 845-857. http://geodesic.mathdoc.fr/item/DMGT_2017_37_4_a0/