We say that a family of $k$-subsets of an $n$-element set is {\it 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.
翻译:我们称一个n元集合的k子集族为{\it 相交族},如果其中任意两个集合相交。本文研究大型相交族的结构。数年前,Han与Kohayakawa(Proc. AMS, 2017),以及随后的Kostochka与Mubayi(Proc. AMS, 2017)获得了关于大型相交族的若干结构结果。本文扩展并推广了他们的结果,给出了结论性的形式。