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arXiv · 2609.27440

Sampling Line-Graph Colorings with Constant Extra Colors

Alireza Haqi
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Abstract

Let $G$ be the line graph of a finite simple graph, with $n\geq1$ vertices and maximum degree $Δ$. We prove that single-site Glauber dynamics for uniform proper $q$-colorings mixes in $O_Δ(n\log(n/\varepsilon))$ steps for every integer $q\geqΔ+5$. Our proof uses the Bochner framework of Chen and Liu (2026).

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Alireza Haqi. 2026-09-23. Sampling Line-Graph Colorings with Constant Extra Colors. https://arxiv.org/abs/2609.27440

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