Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

Erdős–Ko–Rado for random hypergraphs : asymptotics and stability

Tools
- Tools
+ Tools

Gauy, Marcelo M., Han, Hiep and Oliveira, Igor C. (2017) Erdős–Ko–Rado for random hypergraphs : asymptotics and stability. Combinatorics, Probability and Computing, 26 (3). pp. 406-422. doi:10.1017/S0963548316000420

[img]
Preview
PDF
WRAP-Erdős–Ko–Rado-random-hypergraphs-asymptotics-stability-Oliveira-2017.pdf - Accepted Version - Requires a PDF viewer.

Download (762Kb) | Preview
Official URL: http://dx.doi.org/10.1017/S0963548316000420

Request Changes to record.

Abstract

We investigate the asymptotic version of the Erdo˝s-Ko-Rado theorem for the random kuniform hypergraph Hk(n,p). For 2 ≤ k(n) ≤ n/2, let N =(n k)and D =(n−k k). We show thatwith probability tending to 1 as n →∞, the largest intersecting subhypergraph of Hk(n,p) hassize (1 + o(1))pk nN, for any p ≫ n k ln2(n k)D−1. This lower bound on p is asymptotically bestpossible for k = Θ(n). For this range of k and p, we are able to show stability as well. A different behavior occurs when k = o(n). In this case, the lower bound on p is almost optimal. Further, for the small interval D−1 ≪ p ≤ (n/k)1−εD−1, the largest intersecting subhypergraph of Hk(n,p) has size Θ(ln(pD)ND−1), provided that k ≫√nlnn. Together with previous work of Balogh, Bohman and Mubayi, these results settle the asymptotic size of the largest intersecting family in Hk(n,p), for essentially all values of p and k.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Computer Science
Library of Congress Subject Headings (LCSH): Hypergraphs, Graph theory, Asymptotic expansions, Combinatorial analysis
Journal or Publication Title: Combinatorics, Probability and Computing
Publisher: Cambridge University Press
ISSN: 0963-5483
Official Date: May 2017
Dates:
DateEvent
May 2017Published
29 March 2017Available
20 November 2015Accepted
Volume: 26
Number: 3
Page Range: pp. 406-422
DOI: 10.1017/S0963548316000420
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights): This article has been published in a revised form in Combinatorics, Probability and Computing http://doi.org/10.1017/S0963548316000420. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Cambridge University Press 2017
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
132238/2012-8Conselho Nacional de Desenvolvimento Científico e Tecnológicohttp://dx.doi.org/10.13039/501100003593
248952/2013-7Conselho Nacional de Desenvolvimento Científico e Tecnológicohttp://dx.doi.org/10.13039/501100003593
ICM/FIC RC130003Núcleo Milenio Información y Coordinación en Redes, ICRUNSPECIFIED
1115091Fondo Nacional de Desarrollo Científico y Tecnológicohttp://dx.doi.org/10.13039/501100002850
2010/16526-3Fundação de Amparo à Pesquisa do Estado de São Paulohttps://viaf.org/viaf/147398725/#Fundação_de_Amparo_à_Pesquisa_do_Estado_de_São_Paulo
2103/03447-6Fundação de Amparo à Pesquisa do Estado de São Paulohttps://viaf.org/viaf/147398725/#Fundação_de_Amparo_à_Pesquisa_do_Estado_de_São_Paulo
2013/11353-1Fundação de Amparo à Pesquisa do Estado de São Paulohttps://viaf.org/viaf/147398725/#Fundação_de_Amparo_à_Pesquisa_do_Estado_de_São_Paulo
430/15Coordenação de Aperfeiçoamento de Pessoal de Nível Superiorhttps://viaf.org/viaf/219588473/#CAPES_(Organization_:_Brazil)
200252/2015-1Conselho Nacional de Desenvolvimento Científico e Tecnológicohttp://dx.doi.org/10.13039/501100003593

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics

twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us