eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2006-01-01
Vol. 8
10.46298/dmtcs.360
360
journal article
On randomly colouring locally sparse graphs
Alan Frieze
https://orcid.org/0000-0002-8481-5615
Juan Vera
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 #x226a 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 #x2248 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 #x226a 1, this beats the 11Δ /6 bound of Vigoda for general graphs.
https://dmtcs.episciences.org/360/pdf
Counting Colourings
Sampling
Markov Chains
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]