Very rapidly mixing Markov chains for 2?-colorings and for independent sets in a graph with maximum degree 4

Abstract

We introduce a new technique for analyzing the mixing rate of Markov chains. We use it to prove that the Glauber dynamics on 2Δ-colorings of a graph with maximum degree Δ mixes in O(n log n) time. We prove the same mixing rate for the Insert/Delete/Drag chain of Dyer and Greenhill (Random Structures Algorithms13, 285–317 (1998)) on independent sets of graphs with maximum degree 4. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 18: 101–115, 2001