Regular Intersecting Families

2017/09/29 by Ihringer, Ferdinand, Kupavskii, Andrey
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.10462

Abstract

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(n-1\choose k-1) if and only if k=o(n).

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