On systematic scan for sampling H‐colorings of the path

We show that systematic scan for H‐colorings of the n‐vertex path mixes in O(log n) scans for any fixed H using block dynamics. For a restricted family of H we furthermore show that systematic scan mixes in O(log n) scans for any scan order. For completeness we show that a random update Markov chain mixes in O(nlog n) updates for any fixed H. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009