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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Regularity conditions and intersecting hypergraphs


Author: Peter Frankl
Journal: Proc. Amer. Math. Soc. 82 (1981), 309-311
MSC: Primary 05C65; Secondary 05A05, 05C25
MathSciNet review: 609674
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Abstract: Let $ (\mathcal{F},X)$ be a hypergraph with a transitive group of automorphisms. Suppose further that any four edges of $ \mathcal{F}$ intersect nontrivially. Denoting $ \left\vert X \right\vert$ by $ n$ we prove $ \left\vert \mathcal{F} \right\vert = O({2^n})$. We show as well that it is not sufficient to suppose regularity instead of the transitivity of $ \operatorname{Aut} (\mathcal{F})$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0609674-1
PII: S 0002-9939(1981)0609674-1
Article copyright: © Copyright 1981 American Mathematical Society