A Non-Markovian Coupling for Randomly Sampling Colorings

We study a simple Markov chain, known as the Glauber dynamics, for randomly sampling (proper) k-colorings of an input graph G on n vertices with maximum degree ∆ and girth g. We prove the Glauber dynamics is close to the uniform distribution after O(n log n) steps whenever k > (1 + )∆, for all > 0, assuming g ≥ 11 and ∆ = Ω(log n). The best previously known bounds were k > 11∆/6

• Type: Conference
• Year: 2003
• Where: FOCS
• Authors: Thomas P. Hayes, Eric Vigoda
• Keywords: FOCS 2003, Girth G, Glauber Dynamics, Simple Markov Chain, Theoretical Computer Science