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Combinatorics, Complexity, and ChanceA Tribute to Dominic Welsh$
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Geoffrey Grimmett and Colin McDiarmid

Print publication date: 2007

Print ISBN-13: 9780198571278

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198571278.001.0001

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A SURVEY ON THE USE OF MARKOV CHAINS TO RANDOMLY SAMPLE COLOURINGS

A SURVEY ON THE USE OF MARKOV CHAINS TO RANDOMLY SAMPLE COLOURINGS

Chapter:
(p.53) 4 A SURVEY ON THE USE OF MARKOV CHAINS TO RANDOMLY SAMPLE COLOURINGS
Source:
Combinatorics, Complexity, and Chance
Author(s):

Alan Frieze

Eric Vigoda

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198571278.003.0004

In recent years, considerable progress has been made on the analysis of Markov chains for generating a random colouring of an input graph. These improvements have come in conjunction with refinements of the coupling method, which is a classical tool in probability theory. This chapter surveys results on generating random colourings and related technical improvements. It focuses on Markov Chain Monte Carlo (MCMC) algorithms for approximately counting the number of k-colourings of a graph.

Keywords:   Markov chain Monte Carlo algorithms, input graph, random colourings, coupling method, k-colourings

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