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On tournaments with a prescribed property. (English) Zbl 0794.05032
Summary: A round robin tournament on $$q$$ players in which draws are not permitted is said to have property $$P(n,k)$$ if each player in any subset of $$n$$ players is defeated by at leat $$k$$ other players. We consider the problem of determining the minimum value $$f(n,k)$$ such that every tournament of order $$q\geq f(n,k)$$ has property $$P(n,k)$$. The case $$k=1$$ has been studied by P. Erdős, G. and E. Szekeres, R. Graham and J. H. Spencer, and B. Bollobás. In this paper, we present a lower bound on $$f(n,k)$$ for the case of Paley tournaments.

##### MSC:
 05C20 Directed graphs (digraphs), tournaments
##### Keywords:
robin tournament; player; Paley tournaments