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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.

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Article Open access 03 October 2017

L.-C. Zhang & M. Patone

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA. tetali@math.gatech.edu., US

    P. Tetali

  2. Mathematics Department, MIT, Cambridge, MA 02139, USA. vempala@math.mit.edu., US

    S. Vempala

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  1. P. Tetali
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  2. S. Vempala
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Received October 30, 1997; revised March 12, 1999, and April 17, 2000.

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Tetali, P., Vempala, S. Random Sampling of Euler Tours. Algorithmica 30, 376–385 (2001). https://doi.org/10.1007/s00453-001-0018-6

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  • DOI: https://doi.org/10.1007/s00453-001-0018-6

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