# The asymptotic numbers of regular tournaments, Eulerian digraphs and Eulerian oriented graphs

@article{McKay1990TheAN, title={The asymptotic numbers of regular tournaments, Eulerian digraphs and Eulerian oriented graphs}, author={Brendan D. McKay}, journal={Combinatorica}, year={1990}, volume={10}, pages={367-377} }

LetRT(n), ED(n) andEOG(n) be the number of labelled regular tournaments, labelled loop-free simple Eulerian digraphs, and labelled Eulerian oriented simple graphs, respectively, onn vertices. Then, asn→∞,, for anyε>0. The last two families of graphs are also enumerated by their numbers of edges. The proofs use the saddle point method applied to appropriaten-dimensional integrals.

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## 47 Citations

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