Random sampling of Euler tours

  • Prasad Tetali
  • Santosh Vempala
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1269)


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.


Markov Chain Transition System Markov Chain Monte Carlo Method Euler Tour Markov Chain Approach 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Prasad Tetali
    • 1
  • Santosh Vempala
    • 2
  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlanta
  2. 2.School of Computer ScienceCarnegie Mellon UniversityPittsburgh

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