Vol. 8, No. 2, 2019

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A simple proof of the Hilton–Milner theorem

Peter Frankl

Vol. 8 (2019), No. 2, 97–101

Let n 2k 4 be integers and a family of k-subsets of {1,2,,n}. We call intersecting if F F for all F,F, and we call nontrivial if FF = . Strengthening the famous Erdős–Ko–Rado theorem, Hilton and Milner proved that || n1 k1 nk1 k1 + 1 if is nontrivial and intersecting. We provide a proof by injection of this result.

finite sets, intersection, hypergraphs
Mathematical Subject Classification 2010
Primary: 05D05
Received: 9 October 2017
Accepted: 28 May 2018
Published: 20 May 2019
Peter Frankl
Rényi Institute