Abstract
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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References
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McKay, B.D. The asymptotic numbers of regular tournaments, Eulerian digraphs and Eulerian oriented graphs. Combinatorica 10, 367–377 (1990). https://doi.org/10.1007/BF02128671
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DOI: https://doi.org/10.1007/BF02128671