Bounds on the number of Eulerian orientations (original) (raw)

Abstract

We show that each loopless 2_k_-regular undirected graph on_n_ 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 fixed_k_, these ground numbers are best possible.

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Authors and 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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• Received: 03 February 1983
• Issue Date: September 1983
• DOI: https://doi.org/10.1007/BF02579193

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