## 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 hr(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 hr(n) = o(n2) although for every fixed c < 2 one has limn ––> oohr(n)/nc = oo.''
Reviewer:  E.M.Palmer
Classif.:  * 05C30 Enumeration of graphs and maps
05C65 Hypergraphs
Keywords:  uniform hypergraph

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