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