Strong Edge Coloring of a Class of Planar Graphs

A strong edge coloring of a graph G is a proper edge coloring such that no two edges with the same color lie on a path of length 3.The strong edge chromatic number of G is the smallest number of colors required to obtain a strong edge coloring of G,denoted by χ′s(G).We prove that if graph G is planar and g(G)≥14,then χ′s(G)≤ [5Δ2-2Δ+1/4] colors,g(G) indicate the girth of G.