Improved bounds on coloring of graphs

Sokol Ndreca, Aldo Procacci, Benedetto Scoppola

Given a graph $G$ with maximum degree $\Delta \ge 3$, we prove that the acyclic edge chromatic number $a^{\prime }(G)$ of $G$ is such that $a^{\prime }(G)\le \lceil 9.62(\Delta -1)\rceil$. Moreover we prove tha…