Strong edge coloring of graphs with maximum degree $6$

Source abstract

Let $G$ be a graph. Under a strong edge coloring of $G$, every color class is an induced matching. The strong chromatic index of $G$, denoted by $χ'_s(G)$, is the smallest integer $k$ such that $G$ admits a strong edge coloring with $k$ colors. Denote by $Δ(G)$ the maximum degree of $G$. In this paper, we prove that every graph $G$ with $Δ(G)\le 6$ satisfies $χ'_s(G)\le 57$, improving the best known upper bound $60$.