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

Combinatorica volume 10, pages367–377(1990)Cite this article

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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  1. Computer Science Department, Australian National University, GPO Box 4, 2601, ACT, Australia

    Brendan D. McKay

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  1. Brendan D. McKay
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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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AMS subject classification (1980)

  • 05 C 30
  • 05 C 20