Geodesic
On Sets of Arcs Containing No Cycles in a Tournament*
Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 261-264

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

A tournament Tn with n nodes is a complete asymmetric digraph [2]. A set S of arcs of a tournament is called consistent if the tournament contains no oriented cycles composed entirely of arcs of S [1]. The object of this note is to provide a new lower bound for f(n), the greatest integer k such that every tournament with n nodes contains a set of k consistent arcs. Erdös and Moon [1] showed that where [x] denotes the largest integer not exceeding x, and the second inequality holds for any fixed ∈ > 0 and all sufficiently large n. 
Reid, K.B. On Sets of Arcs Containing No Cycles in a Tournament*. Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 261-264. doi: 10.4153/CMB-1969-032-x
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[1] 1. Erdös, P. and Moon, J. W., On sets of consistent arcs in a tournament. Can. Math. Bull. 8 (1965) 269–271. Google Scholar

[2] 2. Harary, F., Norman, R. Z. and Cartwright, D., Structural models: An introduction to the theory of directed graphs. (New York, John Wiley and Sons, 1965). Google Scholar

[3] 3. Kendall, M.G. and Smith, B. B., On the method of paired comparisons. Biometrika 31 (1939) 324–345. Google Scholar

[4] 4. Reid, K.B. and Parker, E. T., Disproof of a conjecture of Erdös and Moser on tournaments. J. Combinatorial Theory (to appear). Google Scholar

[5] 5. Reid, K.B., Structure infinite graphs. Ph.D. Thesis, University of Illinois, 1968. Google Scholar

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