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**Zentralblatt MATH**

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

**Zbl.No: ** 593.05038

**Autor: ** Erdös, Paul; Frankl, P.; Rödl, Vojtech

**Title: ** The asymptotic number of graphs not containing a fixed subgraph and a problem for hypergraphs having no exponent. (In English)

**Source: ** Graphs Comb. 2, 113-121 (1986).

**Review: ** From the authors' abstract: ``Let H be a fixed graph of chromatic number r. It is shown that the number of graphs on n vertices and not containing H as a subgraph is 2^{\binom{n}{2}(1- \frac{1}{r-1}+o(1))}.Let h_{r}(n) denote the maximum number of edges in an r-uniform hypergraph n n vertices and in which the union of any three edges has size greater than 3r-3. It is shown that h_{r}(n) = o(n^{2}) although for every fixed c < 2 one has **lim**_{n ––> oo}h_{r}(n)/n^{c} = oo.''

**Reviewer: ** E.M.Palmer

**Classif.: ** * 05C30 Enumeration of graphs and maps

05C65 Hypergraphs

**Keywords: ** uniform hypergraph

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag