Star edge coloring of graphs with Mad(G)< 14/5

Abstract

A star edge coloring of a graph $G$ is a proper edge coloring such that there is no bicolored path or cycle of length four. The minimum number of colors needed for a graph $G$ to admit a star edge coloring is called the star chromatic index and it is denoted by $\chi_s^{'}(G)$. In this paper, we consider graphs of maximum degree $\Delta \geq 4$ and show that if the maximum average degree of a graph is less than $\frac{14}{5}$ then $\chi_s^{'}(G) \leq 2\Delta + 1$.