Regular Intersecting Families

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

Regular intersecting families

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 vertical bar vertical bar = o(((n-1)(k-1))) if and only if k = o(n). (C) 2019 Published by Elsevier B.V