A new construction of non-extendable intersecting families of sets

被引：0

作者：

Majumder, Kaushik ^{[1
]}

机构：

[1] Indian Stat Inst, RC Bose Ctr Cryptol & Secur, 202 Barrackpore Trunk Rd, Kolkata 700108, India

来源：

ELECTRONIC JOURNAL OF COMBINATORICS | 2016年 / 23卷 / 03期

关键词：

Intersecting family of k-sets; Maximal k-cliques;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In 1975, Lovasz conjectured that any maximal intersecting family of k-sets has at most [(e - 1)k!] blocks, where e is the base of the natural logarithm. This conjecture was disproved in 1996 by Frankl and his co-authors. In this short note, we reprove the result of Frankl et al. using a vastly simplified construction of maximal intersecting families with many blocks. This construction yields a maximal intersecting family G(k) of k-sets whose number of blocks is asymptotic to e(2)(k/2)(k-1) as k -> infinity.

引用

页数：4

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