Geodesic
A Constructive Solution to a Tournament Problem
Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 45-48

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

By a tournament Tn on n vertices, we shall mean a directed graph on n vertices for which every pair of distinct vertices form the endpoints of exactly one directed edge (e.g., see [5]). If x and y are vertices of Tn we say that x dominates y if the edge between x and y is directed from x to y. In 1962, K. Schütte [2] raised the following question: Given k > 0, is there a tournament Tn(k) such that for any set S of k vertices of Tn(k) there is a vertex y which dominates all k elements of S. (Such a tournament will be said to have property Pk .) 
Graham, R. L.; Spencer, J. H. A Constructive Solution to a Tournament Problem. Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 45-48. doi: 10.4153/CMB-1971-007-1
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[1] 1. Burgess, D. A., On character sums and primitive roots, Proc. London Math. Soc. (3) 12 (1962), 179-192. Google Scholar

[2] 2. Erdös, P., Applications of probability to combinatorial problems, Proc. of Colloq. on Combinatorial Methods in Probability Theory, August 1–10 (1962), 90-92. Google Scholar

[3] 3. On a problem in graph theory, Math. Gaz. 47 (1963), 220-223. Google Scholar

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[4] 4?C.M.B. Google Scholar

[5] 5. Moon, J. W., Topics on tournaments, Holt, New York, 1968. Google Scholar

[6] 6. Szekeres, E. and Szekeres, G., On a problem of Schütte and Erdös, Math. Gaz. 49 (1965), 290-293. Google Scholar

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