| author: | 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. |
| ps.gz-source: | dm080107.ps.gz (88 K) |
| ps-source: | dm080107.ps (192 K) |
| pdf-source: | dm080107.pdf (190 K) |
The first source gives you the `gzipped' PostScript, the second the plain PostScript and the third the format for the Adobe accrobat reader. Depending on the installation of your web browser, at least one of these should (after some amount of time) pop up a window for you that shows the full article. If this is not the case, you should contact your system administrator to install your browser correctly.
Due to limitations of your local software, the two formats may show up differently on your screen. If eg you use xpdf to visualize pdf, some of the graphics in the file may not come across. On the other hand, pdf has a capacity of giving links to sections, bibliography and external references that will not appear with PostScript.