On randomly colouring locally sparse graphs

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 Hv induced by the neighbours of v V is where is the maximum degree and > c1 ln n then for sufficiently large c1, this chain mixes rapidly provided q/ > ,

• Type: Journal
• Year: 2006
• Where: DMTCS
• Authors: Alan M. Frieze, Juan Vera
• Keywords: Average Degree, DMTCS 2003, DMTCS 2006, Simple Glauber Dynamics, Subgraph Hv