Randomly colouring simple hypergraphs
Discrete Mathematics
2009-01-26 v1 Data Structures and Algorithms
Abstract
We study the problem of constructing a (near) random proper -colouring of a simple k-uniform hypergraph with n vertices and maximum degree \Delta. (Proper in that no edge is mono-coloured and simple in that two edges have maximum intersection of size one). We give conditions on q,\Delta so that if these conditions are satisfied, Glauber dynamics will converge in O(n\log n) time from a random (improper) start. The interesting thing here is that for k\geq 3 we can take q=o(\D).
Cite
@article{arxiv.0901.3699,
title = {Randomly colouring simple hypergraphs},
author = {Alan Frieze and Pall Melsted},
journal= {arXiv preprint arXiv:0901.3699},
year = {2009}
}