Strong Edge Coloring of Subquartic Graphs

A strong k-edge coloring of a graph G is a mapping \(c: E(G)\rightarrow \{1,2,3,...,k\}\) such that for any two edges e and \(e'\) with distance at most two, \(c(e)\ne c(e')\) . The strong chromatic index of G, written \(\chi '_s(G)\) , is the smallest integer k such that G has a strong k-edge coloring. In this paper, using color exchange method and discharging method, we prove that for a subquartic graph G, \(\chi _s'(G)\le 11\) if \(mad(G)<\frac{8}{3}\) , where \(mad(G)=\max \{\frac{2|E(G)|}{|V(G)|},H\subseteq G\}\) .