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The Cartographer
Sampling Proper Colorings on Line Graphs Using $(1+o(1))Δ$ Colors
July 16, 2023 · Declared Dead · 🏛 Symposium on the Theory of Computing
"No code URL or promise found in abstract"
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Authors
Yulin Wang, Chihao Zhang, Zihan Zhang
arXiv ID
2307.08080
Category
cs.DS: Data Structures & Algorithms
Cross-listed
math.PR
Citations
6
Venue
Symposium on the Theory of Computing
Last Checked
4 months ago
Abstract
We prove that the single-site Glauber dynamics for sampling proper $q$-colorings mixes in $O_Δ(n\log n)$ time on line graphs with $n$ vertices and maximum degree $Δ$ when $q>(1+o(1))Δ$. The main tool in our proof is the matrix trickle-down theorem developed by Abdolazimi, Liu and Oveis Gharan (FOCS, 2021).
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