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**Zentralblatt MATH**

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

**Zbl.No: ** 766.05060

**Autor: ** Erdös, Paul; Füredi, Zoltán; Tuza, Zsolt

**Title: ** Saturated r-uniform hypergraphs. (In English)

**Source: ** Discrete Math. 98, No.2, 95-104 (1991).

**Review: ** The following dual version of Turán's problem is considered: for a given r-uniform hypergraph F, determine the minimum number of edges in an r-uniform hypergraph H on n vertices, such that F\not\subset H but a subhypergraph isomorphic to F occurs whenever a new edge (r- tuple) is added to H. For some types of F we find the exact value of the minimum or describe its asymptotic behavior as n tends to infinity; namely, for H_{r}(r+1,r), H_{r}(2r-2,2) and H_{r}(r+1,3), where H_{r}(p,q) denotes the family of all r-uniform hypergraphs with p vertices and q edges. Several problems remain open.

**Classif.: ** * 05C65 Hypergraphs

05C35 Extremal problems (graph theory)

**Keywords: ** Turán's problem; minimum number; hypergraphs

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag