Intersecting families with covering number 3

2024/05/04 by Kupavskii, Andrey · 1 citation
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.02621

Abstract

A covering number of a family is the size of the smallest set that intersects all sets from the family. In 1978 Frankl determined for n≥ n₀(k) the largest intersecting family of k-element subsets of [n] with covering number 3. In this paper, we essentially settle this problem, showing that the same family is extremal for any k≥ 100 and n>2k.

Cited by

• Extremal t-intersecting families for finite sets with t-covering number at least t+2

Related

• Uniform intersecting families with large covering number
• Extremal t-intersecting families for finite sets with t-covering number at least t+2
• Structure and properties of large intersecting families
• Intersecting families of sets and permutations: a survey
• Non-trivially intersecting multi-part families