Asymptotic Enumeration of Eulerian Circuits in the Complete Graph

We determine the asymptotic behaviour of the number of eulerian circuits in a complete graph of odd order. One corollary of our result is the following. If a maximum random walk, constrained to use each edge at most once, is taken on Kn, then the probability that all the edges are eventually used is asymptotic to e3/4 n−1/2 . Some similar results are obtained about eulerian circuits and spanning trees in random regular tournaments. We also give exact values for up to 21 nodes.

• Type: Journal
• Year: 1998
• Where: CPC
• Authors: Brendan D. McKay, Robert W. Robinson
• Keywords: Asymptotic Behaviour, CPC 1998, Eulerian Circuits, Maximum Random Walk