Randomly coloring sparse random graphs with fewer colors than the maximum degree

We analyze Markov chains for generating a random k-coloring of a random graph Gn,d/n. When the average degree d is constant, a random graph has maximum degree (log n/ log log n), with high probability. We show that, with high probability, an efficient procedure can generate an almost uniformly random k-coloring when k = (log log n/ log log log n), i.e., with many fewer colors than the maximum degree. Previous results hold for a more general class of graphs, but always require more colors than the maximum degree.

• Type: Journal
• Year: 2006
• Where: RSA
• Authors: Martin E. Dyer, Abraham D. Flaxman, Alan M. Frieze, Eric Vigoda
• Keywords: Markov Chains, Random, Random Graph, RSA 2006