Acyclic Edge Coloring of Triangle-Free Toroidal Graphs

Abstract

A proper edge coloring $c$ of a graph $G$ is said to be acyclic if $G$ has no bicolored cycle with respect to $c$. It is proved that every triangle-free toroidal graph $G$ admits an acyclic edge coloring with $(\mathrm{\Delta }(G)+5)$ colors. This generalizes a theorem from $[8]$.