On the kernel of intersecting families

N. Alon; Z. Füredi

doi:10.1007/BF01788533

On the kernel of intersecting families

N. Alon, Z. Füredi

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let ℱ be a t-wise s-intersecting family, i.e., |F₁∩ ... ∩ F_t| ≥ s holds for every t members of ℱ. Then there exists a set Y such that |F₁∩ ... ∩ F_t∩ Y| ≥ s still holds for every F₁,..., F_t∈ℱ. Here exponential lower and upper bounds are proven for the possible sizes of Y.

Original language	English (US)
Pages (from-to)	91-94
Number of pages	4
Journal	Graphs and Combinatorics
Volume	3
Issue number	1
DOIs	https://doi.org/10.1007/BF01788533
State	Published - Dec 1987
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1007/BF01788533

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title = "On the kernel of intersecting families",

abstract = "Let ℱ be a t-wise s-intersecting family, i.e., |F1∩ ... ∩ Ft| ≥ s holds for every t members of ℱ. Then there exists a set Y such that |F1∩ ... ∩ Ft∩ Y| ≥ s still holds for every F1,..., Ft∈ℱ. Here exponential lower and upper bounds are proven for the possible sizes of Y.",

author = "N. Alon and Z. F{\"u}redi",

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doi = "10.1007/BF01788533",

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AU - Füredi, Z.

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N2 - Let ℱ be a t-wise s-intersecting family, i.e., |F1∩ ... ∩ Ft| ≥ s holds for every t members of ℱ. Then there exists a set Y such that |F1∩ ... ∩ Ft∩ Y| ≥ s still holds for every F1,..., Ft∈ℱ. Here exponential lower and upper bounds are proven for the possible sizes of Y.

AB - Let ℱ be a t-wise s-intersecting family, i.e., |F1∩ ... ∩ Ft| ≥ s holds for every t members of ℱ. Then there exists a set Y such that |F1∩ ... ∩ Ft∩ Y| ≥ s still holds for every F1,..., Ft∈ℱ. Here exponential lower and upper bounds are proven for the possible sizes of Y.

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DO - 10.1007/BF01788533

M3 - Article

AN - SCOPUS:0348057821

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IS - 1

ER -

On the kernel of intersecting families

Abstract

All Science Journal Classification (ASJC) codes

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