, Volume 30, Issue 3, pp 376-385

Random Sampling of Euler Tours

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Abstract.

We define a Markov chain on the set of Euler tours of a given Eulerian graph based on transformations first defined by Kotzig in 1966. We prove that the chain is rapidly mixing if the maximum degree in the given graph is 6, thus obtaining an efficient algorithm for sampling and counting the set of Euler tours for such an Eulerian graph.

Received October 30, 1997; revised March 12, 1999, and April 17, 2000.