# 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} }

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.

## Topics from this paper

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