Structure of non-trivial intersecting families
Abstract
We say that a family of k-subsets of an n-element set is intersecting, if any two of its sets intersect. In this paper, we study the structure of large intersecting families. Several years ago, Han and Kohayakawa (Proc. AMS, 2017), and then Kostochka and Mubayi (Proc. AMS, 2017) obtained certain structural results concerning large intersecting families. In this paper, we extend and generalize their results, giving them a conclusive form.
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