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**Zentralblatt MATH**

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

**Zbl.No: ** 728.05059

**Autor: ** Erdös, Paul; Hajnal, András; Tuza, Zsolt

**Title: ** Local constraints ensuring small representing sets. (In English)

**Source: ** J. Comb. Theory, Ser. A 58, No.1, 78-84 (1991).

**Review: ** A set T is said to cover a set system *F* if T meets all members of *F*. We raise the following general problem. Find relations among the natural numbers p,r,s,t, that imply the truth of the following statement: If *F* is an r-uniform set system such that each of its subsystems on at most p elements can be covered with an s-element set, then *F* can be covered with a t-element set. Here we investigate the case s = 1.

**Classif.: ** * 05D15 Transversal (matching) theory

05A05 Combinatorial choice problems

05B40 Packing and covering (combinatorics)

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