On the number of maximal intersecting k-uniform families and further applications of Tuza's set pair method

被引：0

作者：

Nagy, Zoltan Lorant ^{[1
]}

Patkos, Balazs ^{[1
,2
]}

机构：

[1] MTA ELTE Geomet & Algebra Combinator Res Grp, H-1117 Budapest, Hungary

[2] Hungarian Acad Sci, Alfred Renyi Inst Math, Budapest, Hungary

来源：

ELECTRONIC JOURNAL OF COMBINATORICS | 2015年 / 22卷 / 01期

关键词：

SYSTEMS; HYPERGRAPHS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the function M(n, k) which denotes the number of maximal k-uniform intersecting families F subset of (([n])(k)). Improving a bound of Balogh, Das, Delcourt, Liu and Sharifzadeh on M(n, k), we determine the order of magnitude of log M(n, k) by proving that for any fixed k, M(n, k) = n Theta(((2K))) holds. Our proof is based on Tuza's set pair approach. The main idea is to bound the size of the largest possible point set of a crossintersecting system. We also introduce and investigate some related functions and parameters.

引用

页数：10