Bounds on the number of Eulerian orientations

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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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