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On Subtournaments of a Tournament

  • J. W. Moon (a1)
Extract

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.

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References
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1. Beineke, L. W. and Harary, F., The maximum number of strongly connected sub tournaments, Canad. Math. Bull, vol. 8 (1965), 491-498.
2. Camion, P., Chemins et circuits hamiltoniens des graphs complets, C. R. Acad. Sci. Paris 249 (1959), 2151-2152.
3. Colombo, U., Sui circuiti nei grafi completi, Boll. Un. Mat. Ital. 19 (1964), 153-170.
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.
5. Harary, F., Norman, R. and Cartwright, D., Structural Models: An Introduction to the Theory of Directed Graphs (New York, 1965).
6. Kendall, M.G. and Babington Smith, B., On the method of paired comparisons, Biometrika 31 (1940), 324-345.
7. Szele, T., Kombinatorische Untersuchungen űber den gerichteten vollstandigen Graphen, Mat. Fiz. Lapok 50 (1943), 223-256.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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