Asymptotic Enumeration of Eulerian circuits in the Complete Graph
McKay, Brendan; Robinson, Robert W
Description
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 e3/4n-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.
dc.contributor.author | McKay, Brendan | |
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dc.contributor.author | Robinson, Robert W | |
dc.date.accessioned | 2015-12-07T22:17:55Z | |
dc.identifier.issn | 0963-5483 | |
dc.identifier.uri | http://hdl.handle.net/1885/18794 | |
dc.description.abstract | 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 e3/4n-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. | |
dc.publisher | Cambridge University Press | |
dc.source | Combinatorics Probability and Computing | |
dc.title | Asymptotic Enumeration of Eulerian circuits in the Complete Graph | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
dc.date.issued | 1998 | |
local.identifier.absfor | 010104 - Combinatorics and Discrete Mathematics (excl. Physical Combinatorics) | |
local.identifier.ariespublication | u8802668xPUB5 | |
local.type.status | Published Version | |
local.contributor.affiliation | McKay, Brendan, College of Engineering and Computer Science, ANU | |
local.contributor.affiliation | Robinson, Robert W, University of Georgia | |
dc.date.updated | 2015-12-07T08:15:53Z | |
local.identifier.scopusID | 2-s2.0-0542423544 | |
Collections | ANU Research Publications |
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