Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1981-0609674-1
MathSciNet review: 609674
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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})$.


References [Enhancements On Off] (What's this?)

  • [1] A. Brace and D. E. Daykin, Sperner type theorems for finite sets, Bull. Austral. Math. Soc. 5 (1971), 197-202. MR 0292691 (45:1774)
  • [2] P. Erdös, C. Ko and R. Rado, Intersection theorems for finite sets, Quart. J. Math. Oxford Ser. (2) 12 (1961), 313-320. MR 0140419 (25:3839)
  • [3] P. Frankl, Families of finite sets satisfying an intersection condition, Bull. Austral. Math. Soc. 15 (1976), 73-79. MR 0460131 (57:127)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 05C65, 05A05, 05C25

Retrieve articles in all journals with MSC: 05C65, 05A05, 05C25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0609674-1
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society