on randomly colouring locally sparse graphs
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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
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| Authors | ;Alan Frieze;Juan Vera |
| Journal | Proteins |
| Year | 2006 |
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