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Almost all Tournaments are Irreducible

Published online by Cambridge University Press:  20 November 2018

J. W. Moon  and
L. Moser
J. W. Moon
Affiliation:
University of Alberta
L. Moser
Affiliation:
University of Alberta
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Given a set of n points, with each pair of distinct points joined by a line that is oriented towards exactly one of the points, then the resulting configuration is called a (roun-drobin) tournament. A tournament is reducible if the points can be separated into two non-empty subsets, A and B, such that every line that joins a point in A to a point in B is oriented towards the point in B. If a tournament is not reducible it is called irreducible. The object of this note is to derive an approximation for P(n), the probability that a tournament on n point, chosen at random from the set of possible ones, will be irreducible. p(1)=1, by definition.

Type
Notes and Problems
Information
Canadian Mathematical Bulletin , Volume 5 , Issue 1 , January 1962 , pp. 61 - 65
Copyright
Copyright © Canadian Mathematical Society 1962

References

1. Paul, Camion, "Chemins et circuits hamiltoniens des graphes complets", C. R. Acad. Sci. Paris, 249 (1959), 2151-2152.Google Scholar
2. Bernard, Roy, "Sur quelques propriétés des graphes fortement", C. R. Acad. Sci. Paris, 247 (1958), 399-401.Google Scholar