Beyond the Erdős-Ko-Rado theorem

https://doi.org/10.1016/0097-3165(91)90031-BGet rights and content
Under an Elsevier user license
open archive

Abstract

The exact bound in the Erdős-Ko-Rado theorem is known [F, W]. It states that if n ⩾ (t + 1)(kt + 1), and F is a t-intersecting family of k-sets of an n-set (|FF′| ⩾ t for all F, F′ ∈ F),then |F⩽(n−1k−1). Define Ar = {F ⊂ {1, 2, …, n} : |F| = k, |F ∩ {1, 2, …, t + 2r}| ⩾ t + r}. Here it is proved that for n>ctlog(t+1) (kt + 1) one has |F| ⩽ maxr |Ar|.

Cited by (0)

Research supported in part by the Hungarian National Science Foundation Grant 1812. This paper was written while the authors visited A.T. & T. Bell Laboratories, Murray Hill, NJ 07974 and Bell Communications Research Inc., Morristown, NJ 07960.