A new bound on the acyclic edge chromatic index

In this note we obtain a new bound for the acyclic edge chromatic number $a^{\mathrm{\prime }}(G)$ of a graph $G$ with maximum degree $D$ proving that $a’(G)\leq 3.569(D-1)$. To get this result we revisit and slightly modify the method described in [Giotis, Kirousis, Psaromiligkos and Thilikos, Theoretical Computer Science, 66: 40-50, 2017].