On families of finite sets no two of which intersect in a singleton
- 1 August 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 17 (1) , 125-134
- https://doi.org/10.1017/s0004972700025521
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.Keywords
This publication has 2 references indexed in Scilit:
- INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETSThe Quarterly Journal of Mathematics, 1961
- Intersection Theorems for Systems of SetsJournal of the London Mathematical Society, 1960