, Volume 30, Issue 3, pp 376–385

Random Sampling of Euler Tours

  • P. Tetali
  • S. Vempala

DOI: 10.1007/s00453-001-0018-6

Cite this article as:
Tetali, P. & Vempala, S. Algorithmica (2001) 30: 376. doi:10.1007/s00453-001-0018-6


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. 

Copyright information

© Springer-Verlag 2001

Authors and Affiliations

  • P. Tetali
    • 1
  • S. Vempala
    • 2
  1. 1.School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA.
  2. 2.Mathematics Department, MIT, Cambridge, MA 02139, USA.

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