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**Zentralblatt MATH**

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

**Zbl.No: ** 258.05132

**Autor: ** Brown, William G.; Erdös, Paul; Sos, V.T.

**Title: ** Some extremal problems on r-graphs. (In English)

**Source: ** New Direct. Theory Graphs, Proc. third Ann Arbor Conf., Univ. Michigan 1971, 53-63 (1973).

**Review: ** [For the entire collection see Zbl 253.00004.]

The main result of this paper consists of the determination, by ``probabilistic'' methods, of a lower bound for a number f^{(r)}(n; k, \ell) defined to be the smallest integer T such that every selection of T distinct r-subsets from an n-set \Omega includes at least \ell distinct r-subsets of some k-subset of \Omega; (the prefixes refer to cardinality). The bound obtained improves on the authors' earlier results for r = 3.

**Classif.: ** * 05C35 Extremal problems (graph theory)

04A20 Combinatorial set theory

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