Bounds on the number of Eulerian orientations

Combinatorica volume 3, pages375–380(1983)Cite this article

Abstract

We show that each loopless 2k-regular undirected graph onn vertices has at least\(\left( {2^{ - k} \left( {_k^{2k} } \right)} \right)^n \) and at most\(\sqrt {\left( {_k^{2k} } \right)^n } \) eulerian orientations, and that, for each fixedk, these ground numbers are best possible.

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Affiliations

  1. Department of Econometrics, Tilburg University, P.O. Box. 90153, 5000, LE Tilburg, The Netherlands

    A. Schrijver

  2. Mathematical Centre, Kruislaan 413, 1098, SJ Amsterdam, The Netherlands

    A. Schrijver

Authors
  1. A. Schrijver
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Dedicated to Paul Erdős on his seventieth birthday

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Schrijver, A. Bounds on the number of Eulerian orientations. Combinatorica 3, 375–380 (1983). https://doi.org/10.1007/BF02579193

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AMS subject classification (1980)

  • 05 C 45
  • 05 C 30
  • 15 A 15