Bounds on the number of Eulerian orientations

@article{Schrijver1983BoundsOT,
  title={Bounds on the number of Eulerian orientations},
  author={Alexander Schrijver},
  journal={Combinatorica},
  year={1983},
  volume={3},
  pages={375-380}
}
  • A. Schrijver
  • Published 1983
  • Mathematics, Computer Science
  • Combinatorica
AbstractWe 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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