List-Edge-Coloring with Bounded Maximum Degree

Abstract

For a graph $G$, we show that if $mad(G)<m$, then ${\chi }_{\ell }^{\prime }(G)\le \Delta +1$ where $m$ depends upon $\Delta$ and ${\chi }_{\ell }^{\prime }(G)$ is the list-chromatic index of $G$. When $\Delta \le 20$ the value of $m$ is close to $\frac{1}{2}\Delta$, but as $\Delta$ increases $m$ becomes asymptotic to about $\frac{1}{4}\Delta +5$.