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(G) − 2 when Δ(G) ≥ 6 and 𝜒's(G) ≤ 19 when Δ(G) = 5, where g is the girth of G.
@article{bwmeta1.element.doi-10_7151_dmgt_1951,
author = {Wen-Yao Song and Lian-Ying Miao},
title = {Strong Edge-Coloring Of Planar Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {845-857},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1951}
}
Wen-Yao Song; Lian-Ying Miao. Strong Edge-Coloring Of Planar Graphs. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 845-857. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1951/