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**Zentralblatt MATH**

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

**Zbl.No: ** 493.05048

**Autor: ** Chung, F.R.K.; Erdös, Paul; Graham, Ronald L.

**Title: ** Minimal decompositions of hypergraphs into mutually isomorphic subhypergraphs. (In English)

**Source: ** J. Comb. Theory, Ser. A 32, 241-251 (1982).

**Review: ** The authors tackle the following problem: given a family**{**H_{1},...,H_{k}**}** of r-uniform hypergraphs, each with the same number of edges, find the smallest t such that each H_{i} can be decomposed into mutually isomorphic subhypergraphs E_{ij},1 \leq j \leq t. This study extends the authors' previous work on the case r = 2 [Combinatorica 1, 13-24 (1981)]. The main techniques used are interesting counting arguments. The results obtained are good but not sharp, so many open problems remain.

**Reviewer: ** D.de Caen

**Classif.: ** * 05C65 Hypergraphs

**Keywords: ** uniform hypergraphs; decompositions into isomorphic subhypergraphs

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