Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T06:43:40.065Z Has data issue: false hasContentIssue false

On Subtournaments of a Tournament

Published online by Cambridge University Press:  20 November 2018

J. W. Moon*
Affiliation:
University of Alberta, Edmonton
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Beineke and Harary [l] recently showed that the maximum number of strong tournaments with k nodes that can be contained in a tournament with n nodes is

if 3 ≤ k ≤ n. The object of this note is to obtain some additional results of this type. We will use essentially the same terminology as was used in [ l ], so we will not repeat the standard definitions here.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Beineke, L. W. and Harary, F., The maximum number of strongly connected sub tournaments, Canad. Math. Bull, vol. 8 (1965), 491-498.Google Scholar
2. Camion, P., Chemins et circuits hamiltoniens des graphs complets, C. R. Acad. Sci. Paris 249 (1959), 2151-2152.Google Scholar
3. Colombo, U., Sui circuiti nei grafi completi, Boll. Un. Mat. Ital. 19 (1964), 153-170.Google Scholar
4. Erdős, P. and Moser, L., On the representation of directed graphs as unions or orderings, Publi. Math. Inst. Hung. Acad. Sci. 9 (1964), 125-132.Google Scholar
5. Harary, F., Norman, R. and Cartwright, D., Structural Models: An Introduction to the Theory of Directed Graphs (New York, 1965).Google Scholar
6. Kendall, M.G. and Babington Smith, B., On the method of paired comparisons, Biometrika 31 (1940), 324-345.Google Scholar
7. Szele, T., Kombinatorische Untersuchungen űber den gerichteten vollstandigen Graphen, Mat. Fiz. Lapok 50 (1943), 223-256.Google Scholar