Dyer, M, Frieze, A, Hayes, TP et al. (1 more author) (2013) Randomly Coloring Constant Degree Graphs. Random Structures and Algorithms, 43 (2). 181 - 200. ISSN 1042-9832
Abstract
We study a simple Markov chain, known as the Glauber dynamics, for generating a random k-coloring of an n-vertex graph with maximum degree Δ. We prove that, for every ε > 0, the dynamics converges to a random coloring within O(nlog n) steps assuming k ≥ k 0 (ε) and either: (i) k/Δ > α* + ε where α*≈≈ 1.763 and the girth g ≥ 5, or (ii) k/Δ >β * + ε where β*≈≈ 1.489 and the girth g ≥ 7. Our work improves upon, and builds on, previous results which have similar restrictions on k/Δ and the minimum girth but also required Δ = Ω (log n). The best known result for general graphs is O(nlog n) mixing time when k/Δ > 2 and O(n2) mixing time when k/Δ > 11/6. Related results of Goldberg et al apply when k/Δ > α* for all Δ ≥ 3 on triangle-free "neighborhood-amenable" graphs.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Keywords: | Glauber dynamics; Random colorings; Coupling Technique |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 Sep 2013 10:22 |
Last Modified: | 15 Sep 2014 03:04 |
Published Version: | http://dx.doi.org/10.1002/rsa.20451 |
Status: | Published |
Publisher: | Wiley-Blackwell |
Identification Number: | 10.1002/rsa.20451 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:76430 |