On families of finite sets no two of which intersect in a singleton-Reference-Cited by-同舟云学术

On families of finite sets no two of which intersect in a singleton

Published:1977-08 Issue:1 Volume:17 Page:125-134
ISSN:0004-9727
Container-title:Bulletin of the Australian Mathematical Society
language:en
Short-container-title:Bull. Austral. Math. Soc.

Author:

Frankl Peter

Abstract

Let X be a finite set of cardinality n, and let F be a family of k-subsets of X. In this paper we prove the following conjecture of P. Erdös and V.T. Sós.If n > n0(k), k ≥ 4, then we can find two members F and G in F such that |F ∩ G| = 1.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference5 articles.

1. INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS

2. [5] Katona Gyula (unpublished).

3. [2] Erdös P. , “Problems and results in graph theory and combinatorial analysis”, Proa. Fifth British Combinatorial Conference, 1975, 169–172 (University of Aberdeen, Aberdeen, 1975. Congressus Numerantium, 15. Utilitas Mathematica, Winnipeg, 1976).

4. Intersection Theorems for Systems of Sets

5. A problem on independent r-tuples;Erdös;Ann. Univ. Sci. Budapest. Eötvös Sect. Math.,1965

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