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- W2762912304 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 different extremal properties of intersecting families, as well as the structure of large intersecting families. We also give some results on $k$-uniform families without $s$ pairwise disjoint sets, related to the Erdős Matching Conjecture. We prove a conclusive version of Frankl's theorem on intersecting families with bounded maximal degree. This theorem, along with its generalizations to cross-intersecting families, implies many results on the topic, obtained by Frankl, Frankl and Tokushige, Kupavskii and Zakharov and others. We study the structure of large intersecting families, obtaining some general structural theorems which generalize the results of Han and Kohayakawa, as well as Kostochka and Mubayi. We give degree and subset degree version of the Erdős--Ko--Rado and the Hilton--Milner theorems, extending the results of Huang and Zhao, and Frankl, Han, Huang and Zhao. We also extend the range in which the degree version of the Erdős Matching conjecture holds." @default.
- W2762912304 created "2017-10-20" @default.
- W2762912304 creator A5048570599 @default.
- W2762912304 date "2018-10-01" @default.
- W2762912304 modified "2023-09-27" @default.
- W2762912304 title "Structure and properties of large intersecting families" @default.
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