On cross-intersecting families of sets

Christian Bey

doi:10.1007/s00373-004-0598-4

On cross-intersecting families of sets

Christian Bey^*

^*Corresponding author for this work

Institute of Mathematics

18 Citations (Scopus)

Abstract

A family ℓ-element subsets and a family κ-element subsets of an n-element set are cross-intersecting if every set from A has a nonempty intersection with every set from B. We compare two previously established inequalities each related to the maximization of the product |A||ℬ|, and give a new and short proof for one of them. We also determine the maximum of |A|ω_l + |ℬ|ω_k for arbitrary positive weights ω_ℓ,ω _κ .

Original language	English
Journal	Graphs and Combinatorics
Volume	21
Issue number	2
Pages (from-to)	161-168
Number of pages	8
ISSN	0911-0119
DOIs	https://doi.org/10.1007/s00373-004-0598-4
Publication status	Published - 01.06.2005

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AB - A family ℓ-element subsets and a family κ-element subsets of an n-element set are cross-intersecting if every set from A has a nonempty intersection with every set from B. We compare two previously established inequalities each related to the maximization of the product |A||ℬ|, and give a new and short proof for one of them. We also determine the maximum of |A|ωl + |ℬ|ωk for arbitrary positive weights ωℓ,ω κ .

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On cross-intersecting families of sets

Abstract

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