List-Edge-Coloring with Bounded Maximum Degree

TL;DR

This paper establishes bounds on the list-chromatic index of graphs with bounded maximum average degree, showing it is at most one more than the maximum degree under certain conditions, with bounds depending on the maximum degree.

Contribution

The paper provides new bounds relating maximum average degree and list-chromatic index, extending understanding of edge-coloring in graphs with bounded average degree.

Findings

For graphs with mad(G)<m, the list-chromatic index is at most Δ+1.

When Δ ≤ 20, m is close to 0.5Δ; for larger Δ, m approaches 0.25Δ+5.

The bounds improve existing results on list-edge-coloring with degree constraints.

Abstract

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