Sampling Line-Graph Colorings with Constant Extra Colors

Let $G$ be the line graph of a finite simple graph, with $n\ge 1$ vertices and maximum degree $\mathrm{\Delta }$. We prove that single-site Glauber dynamics for uniform proper $q$-colorings mixes in $O_{\mathrm{\Delta }}(n\log (n\mathrm{/}\epsilon ))$ steps for every integer $q\ge \mathrm{\Delta }+5$. Our proof uses the Bochner framework of Chen and Liu (2026).