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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 848.05049

**Autor: ** Erdös, Paul; Fon-Der-Flaas, D.; Kostochka, A.V.; Tuza, Zs.

**Title: ** Small transversals in uniform hypergraphs. (In English)

**Source: ** Sib. Adv. Math. 2, No.1, 82-88 (1992).

**Review: ** Suppose that in a collection H of r-element sets, for any p sets there is a set of at most t elements that meets all of them. We study the following problem: find a sharp upper bound f(r,p,t) on the cardinality of a smallest set meeting all members of H. We determine the exact values of f(r,p,2) for p \leq 6 and every r, of f(r,t+1,t) and f(r,t+2, t) for every r and t, and prove that f(r,p,t) = O(rp^{- 1/t}) for every fixed t when r,p ––> oo.

**Classif.: ** * 05C65 Hypergraphs

**Keywords: ** hypergraph; transversal

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