10.46298/dmtcs.360
https://dmtcs.episciences.org/360
Frieze, Alan
Alan
Frieze
0000-0002-8481-5615
Vera, Juan
Juan
Vera
National Science Foundation
0200945
Probabilistic Considerations in the Analysis of Algorithms
On randomly colouring locally sparse graphs
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.
episciences.org
Counting Colourings
Sampling
Markov Chains
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
2015-06-09
2006-01-01
2006-01-01
en
journal article
https://hal.science/hal-00961105v1
1365-8050
https://dmtcs.episciences.org/360/pdf
VoR
application/pdf
Discrete Mathematics & Theoretical Computer Science
Vol. 8
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