### Volume 8

n° 1 (2006), pp. 121-128author: | Alan Frieze and Juan Vera |
---|---|

title: | On randomly colouring locally sparse graphs |

keywords: | Counting Colourings, Sampling, Markov Chains |

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 induced by
the neighbours of v v ∈ V
is ≪Δ where Δ is the maximum degree and Δ>c then for sufficiently large 1 ln nc ,
this chain mixes rapidly provided 1 q/Δ>α , where α≈ 1.763 is the root of α = e .
For this class of graphs, which includes planar graphs, triangle free graphs and random
graphs {1/α} G with {n,p} p ≪ 1 ,
this beats the 11Δ/6 bound of
Vigoda for general graphs. |

If your browser does not display the abstract correctly (because of the different mathematical symbols) you may look it up in the PostScript or PDF files. | |

reference: | Alan Frieze and Juan Vera (2006),
On randomly colouring locally sparse graphs,
Discrete Mathematics and Theoretical Computer Science 8, pp. 121-128 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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Automatically produced on Fri Apr 14 22:25:33 CEST 2006 by falk