, Volume 30, Issue 3, pp 376-385

First online:

Random Sampling of Euler Tours

  • P. TetaliAffiliated withSchool of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA.
  • , S. VempalaAffiliated withMathematics Department, MIT, Cambridge, MA 02139, USA.

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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.

Key words. Euler tours, Random sampling, Random walk.