on randomly colouring locally sparse graphs

Clicks: 31
ID: 225397
2006
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Abstract
We consider the problem of generating a random q-colouring of a graph G=(V,E). We consider the simple Glauber Dynamics chain. We show that if for all v ∈ V the average degree of the subgraph H v induced by the neighbours of v ∈ V is ≪Δ where Δ is the maximum degree and Δ>c 1 ln n then for sufficiently large c 1, this chain mixes rapidly provided q/Δ>α, where α≈ 1.763 is the root of α = e {1/α}. For this class of graphs, which includes planar graphs, triangle free graphs and random graphs G {n,p} with p ≪ 1, this beats the 11Δ/6 bound of Vigoda for general graphs.
Reference Key
frieze2006discreteon Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Alan Frieze, Juan Vera
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Journal Proteins
Year 2006
DOI
DOI not found
URL
http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/496
Keywords
mathematics

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