We call a family of sets intersecting, if any two sets in the family
intersect. In this paper we investigate intersecting families F of
k-element subsets of [n]:={1,…,n}, such that every element of [n]
lies in the same (or approximately the same) number of members of
F. In particular, we show that we can guarantee ∣F∣=o((k−1n−1)) if and only if k=o(n).Comment: 15 pages, accepted versio