Intersecting families of sets are typically trivial

被引：1

作者：

Balogh, Jozsef ^{[1
]}

Garcia, Ramon I. ^{[2
]}

Li, Lina ^{[3
]}

Wagner, Adam Zsolt ^{[4
]}

机构：

[1] Univ Illinois, Dept Math Sci, Champaign, IL 61801 USA

[2] Univ Illinois, Dept Math, Urbana, IL USA

[3] Univ Waterloo, Dept Combinator & Optimizat, Waterloo, ON, Canada

[4] Worcester Polytech Inst, Dept Math Sci, Worcester, MA USA

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES B | 2024年 / 164卷

关键词：

Extremal combinatorics; Intersecting family; Graph container method; INDEPENDENT SETS; THEOREMS; SYSTEMS;

D O I：

10.1016/j.jctb.2023.09.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A family of subsets of [n] is intersecting if every pair of its sets intersects. Determining the structure of large intersecting families is a central problem in extremal combinatorics. Frankl- Kupavskii and Balogh-Das-Liu-Sharifzadeh-Tran showed that for n >= 2k + c root k ln k, almost all k-uniform intersecting families are stars. Improving their result, we show that the same conclusion holds for n >= 2k + 100 ln k. Our proof uses, among others, the graph container method and the Das-Tran removal lemma.(c) 2023 Elsevier Inc. All rights reserved.

引用

页码：44 / 67

页数：24

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