Maximal 3-Wise Intersecting Families

被引：0

作者：

Balogh, Jozsef ^{[1
]}

Chen, Ce ^{[1
]}

Hendrey, Kevin ^{[2
]}

Lund, Ben ^{[2
]}

Luo, Haoran ^{[1
]}

Tompkins, Casey ^{[3
]}

Tran, Tuan ^{[4
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[2] Inst Basic Sci IBS, Discrete Math Grp, Daejeon, South Korea

[3] Hungarian Acad Sci, Alfred Reny Inst Math, Budapest, Hungary

[4] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

来源：

COMBINATORICA | 2023年 / 43卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Intersecting; Set-system; Maximal; Saturation; GRAPHS; PAIRS;

D O I：

10.1007/s00493-023-00046-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A family .7' on ground set [n] := {1, 2, ... , n} is maximal k -wise intersecting if every collection of at most k sets in .7' has non-empty intersection, and no other set can be added to .7' while maintaining this property. In 1974, Erdos and Kleitman asked for the minimum size of a maximal k-wise intersecting family. We answer their question for k = 3 and sufficiently large n. We show that the unique minimum family is obtained by partitioning the ground set [n] into two sets A and B with almost equal sizes and taking the family consisting of all the proper supersets of A and of B.

引用

页码：1045 / 1066

页数：22

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