Strong Edge-Coloring Of Planar Graphs

• Main Authors: Song Wen-Yao, Miao Lian-Ying
• Format: Article
• Language: English
• Published: Sciendo 2017-11-01
• Series: Discussiones Mathematicae Graph Theory
• Subjects: strong edge-coloring; strong chromatic index; planar graph; dis- charging method.
• Online Access: https://doi.org/10.7151/dmgt.1951

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.