Maximum Hitting for n Sufficiently Large

Ben Barber

doi:10.1007/s00373-012-1281-9

Maximum Hitting for n Sufficiently Large

Ben Barber

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

For a left-compressed intersecting family A⊆[n]^(r) and a set X⊆[n] , let A(X)={A∈A:A∩X≠∅} . Borg asked: for which X is |A(X)| maximised by taking A to be all r-sets containing the element 1? We determine exactly which X have this property, for n sufficiently large depending on r.

Original language	English
Pages (from-to)	267-274
Number of pages	8
Journal	Graphs and Combinatorics
Volume	30
Issue number	2
Early online date	16 Jan 2013
DOIs	https://doi.org/10.1007/s00373-012-1281-9
Publication status	Published - Mar 2014

Keywords

Intersecting family
Compression
Generating set
Erdős–Ko–Rado theorem

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10.1007/s00373-012-1281-9

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This is the accepted author manuscript (AAM). The final published version (version of record) is available online via Springer Verlag at http://dx.doi.org/10.1007/s00373-012-1281-9. Please refer to any applicable terms of use of the publisher.
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abstract = "For a left-compressed intersecting family A⊆[n](r) and a set X⊆[n] , let A(X)={A∈A:A∩X≠∅} . Borg asked: for which X is |A(X)| maximised by taking A to be all r-sets containing the element 1? We determine exactly which X have this property, for n sufficiently large depending on r.",

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AB - For a left-compressed intersecting family A⊆[n](r) and a set X⊆[n] , let A(X)={A∈A:A∩X≠∅} . Borg asked: for which X is |A(X)| maximised by taking A to be all r-sets containing the element 1? We determine exactly which X have this property, for n sufficiently large depending on r.

KW - Intersecting family

KW - Compression

KW - Generating set

KW - Erdős–Ko–Rado theorem

U2 - 10.1007/s00373-012-1281-9

DO - 10.1007/s00373-012-1281-9

M3 - Article (Academic Journal)

SN - 0911-0119

VL - 30

SP - 267

EP - 274

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

IS - 2

ER -

Maximum Hitting for n Sufficiently Large

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Keywords

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