Geodesic
The Maximum Number of Strongly Connected Subtournaments*
Canadian mathematical bulletin, Tome 8 (1965) no. 4, pp. 491-498

Voir la notice de l'article provenant de la source Cambridge University Press

In the ranking of a collection of p objects by the method of paired comparisons, a measure of consistency is provided by the relative number of transitive (or consistent) triples and cyclic (or inconsistent) triples. This point of view was introduced by Kendall and Babington Smith [4]. They found a formula for the maximum number of cyclic triples, thereby determining the greatest inconsistency possible. The purpose of this note is to extend the result to obtain the maximum number of "strongly connected" collections of n objects among the given p objects. 
Beineke, Lowell W.; Harary, Frank. The Maximum Number of Strongly Connected Subtournaments*. Canadian mathematical bulletin, Tome 8 (1965) no. 4, pp. 491-498. doi: 10.4153/CMB-1965-035-x
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[1] 1. Berge, C., Théorie des graphes et ses applications, Paris, Dunod, 1958. Google Scholar

[2] 2. Harary, F. and Moser, L., The theory of round robin tournaments, Amer. Math. Monthly, to appear. Google Scholar

[3] 3. Harary, F., Norman, R., and Cartwright, D., Structural models: an introduction to the theory of directed graphs, New York, 1965. Google Scholar

[4] 4. Kendall, M. G. and Babington Smith, B., On the method of paired comparisons, Biometrika, 31 (1940) 324-345. Google Scholar

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