, Volume 3, Issue 3-4, pp 375-380

Bounds on the number of Eulerian orientations

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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.

Dedicated to Paul Erdős on his seventieth birthday