# 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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