## 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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