Barber, B. Graphs and Combinatorics (2014) 30: 267. PDF
Borg asked what happens to the Erdős-Ko-Rado theorem if we only count sets meeting some fixed set 
, and answered the question for 
, the size of the sets in the set family. This paper answers the question for 
, provided 
, the size of the ground set, is sufficiently large.
There is a typo in the proof of Theorem 4 in the journal version. The line beginning “By Lemma 9, 
has size polynomial in …” should read “By Lemma 9, 
…”. Thanks to Candida Bowtell for spotting this.