Very rapid mixing of the Glauber dynamics for proper colorings on bounded-degree graphs

Authors:
Martin Dyer;Catherine Greenhill;Mike Molloy
Affiliations:
School of Computing, University of Leeds, Leeds LS2 9JT, UK;Department of Mathematics and Statistics, University of Melbourne, Parkville, Vic. 3010, Australia;Department of Computer Science, University of Toronto, Toronto, Canada
Venue:
Random Structures & Algorithms
Year:
2002

Citing 8
Cited 5

A very simple algorithm for estimating the number of k-colorings of a low-degree graph

Random Structures & Algorithms
A more rapidly mixing Markov chain for graph colorings

proceedings of the eighth international conference on Random structures and algorithms
Delayed path coupling and generating random permutations via distributed stochastic processes

Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Beating the 2&Dgr; bound for approximately counting colourings: a computer-assisted proof of rapid mixing

Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Coupling vs. conductance for the Jerrum-Sinclair chain

Random Structures & Algorithms
Very rapidly mixing Markov Chains for 2&Dgr;-colorings and for independent sets in a graph with maximum degree 4

Random Structures & Algorithms
An Extension of Path Coupling and Its Application to the Glauber Dynamics for Graph Colorings

SIAM Journal on Computing
Path coupling: A technique for proving rapid mixing in Markov chains

FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science

The Glauber dynamics on colourings of a graph with high girth and maximum degree

STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Randomly coloring graphs of girth at least five

Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Variable length path coupling

SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Variable length path coupling

Random Structures & Algorithms
Approximate counting via correlation decay in spin systems

Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

Recent results have shown that the Glauber dynamics for graph colorings has optimal mixing time when (i) the graph is triangle-free and Δ-regular and the number of colors k is a small constant fraction smaller than 2Δ, or (ii) the graph has maximum degree Δ and k = 2Δ. We extend both these results to prove that the Glauber dynamics has optimal mixing time when the graph has maximum degree Δ and the number of colors is a small constant fraction smaller than 2Δ.