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

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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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