The number of irreducible tournaments
Glasgow mathematical journal, Tome 11 (1970) no. 2, pp. 97-101
Voir la notice de l'article provenant de la source Cambridge University Press
An n-tournament is a set of n labelled points, each pair A, B of which is joined either by the oriented line AB or by the oriented line BA. There are N = n(n –1)/2 such pairs and so Fn different n-tournaments, where Fn = 2N. A tournament is reducible if the points can be separated into two non-empty subsets and B, such that every line joining a point in to a point in B is directed towards the point in B. Rado [3] showed that an irreducible tournamentis strongly connected; i.e. for every ordered pair of points A, B, there is a sequence of correctly oriented lines AC1, C1C2, ..., ChB in the tournament, and conversely that a strongly connected tournament is irreducible.
Wright, E. M. The number of irreducible tournaments. Glasgow mathematical journal, Tome 11 (1970) no. 2, pp. 97-101. doi: 10.1017/S0017089500000914
@article{10_1017_S0017089500000914,
author = {Wright, E. M.},
title = {The number of irreducible tournaments},
journal = {Glasgow mathematical journal},
pages = {97--101},
year = {1970},
volume = {11},
number = {2},
doi = {10.1017/S0017089500000914},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500000914/}
}
[1] 1.Moon, J. W. and Moser, L., Almost all tournaments are irreducible, Canadian Math. Bull. 5 (1962), 61–65. Google Scholar | DOI
[2] 2.Moon, J. W., Topics on tournaments (New York, 1968). Google Scholar
[3] 3.Rado, R., Theorems on linear combinatorial topology and general measure, Ann. of Math. 44 (1943), 228–270. Google Scholar | DOI
Cité par Sources :