---
_id: '12286'
abstract:
- lang: eng
  text: "Inspired by the study of loose cycles in hypergraphs, we define the loose
    core in hypergraphs as a structurewhich mirrors the close relationship between
    cycles and $2$-cores in graphs. We prove that in the $r$-uniform binomial random
    hypergraph $H^r(n,p)$, the order of the loose core undergoes a phase transition
    at a certain critical threshold and determine this order, as well as the number
    of edges, asymptotically in the subcritical and supercritical regimes.
\r\nOur
    main tool is an algorithm called CoreConstruct, which enables us to analyse a
    peeling process for the loose core. By analysing this algorithm we determine the
    asymptotic degree distribution of vertices in the loose core and in particular
    how many vertices and edges the loose core contains. As a corollary we obtain
    an improved upper bound on the length of the longest loose cycle in $H^r(n,p)$."
acknowledgement: 'Supported by Austrian Science Fund (FWF): I3747, W1230.'
article_number: P4.13
article_processing_charge: No
article_type: original
author:
- first_name: Oliver
  full_name: Cooley, Oliver
  id: 43f4ddd0-a46b-11ec-8df6-ef3703bd721d
  last_name: Cooley
- first_name: Mihyun
  full_name: Kang, Mihyun
  last_name: Kang
- first_name: Julian
  full_name: Zalla, Julian
  last_name: Zalla
citation:
  ama: Cooley O, Kang M, Zalla J. Loose cores and cycles in random hypergraphs. <i>The
    Electronic Journal of Combinatorics</i>. 2022;29(4). doi:<a href="https://doi.org/10.37236/10794">10.37236/10794</a>
  apa: Cooley, O., Kang, M., &#38; Zalla, J. (2022). Loose cores and cycles in random
    hypergraphs. <i>The Electronic Journal of Combinatorics</i>. The Electronic Journal
    of Combinatorics. <a href="https://doi.org/10.37236/10794">https://doi.org/10.37236/10794</a>
  chicago: Cooley, Oliver, Mihyun Kang, and Julian Zalla. “Loose Cores and Cycles
    in Random Hypergraphs.” <i>The Electronic Journal of Combinatorics</i>. The Electronic
    Journal of Combinatorics, 2022. <a href="https://doi.org/10.37236/10794">https://doi.org/10.37236/10794</a>.
  ieee: O. Cooley, M. Kang, and J. Zalla, “Loose cores and cycles in random hypergraphs,”
    <i>The Electronic Journal of Combinatorics</i>, vol. 29, no. 4. The Electronic
    Journal of Combinatorics, 2022.
  ista: Cooley O, Kang M, Zalla J. 2022. Loose cores and cycles in random hypergraphs.
    The Electronic Journal of Combinatorics. 29(4), P4.13.
  mla: Cooley, Oliver, et al. “Loose Cores and Cycles in Random Hypergraphs.” <i>The
    Electronic Journal of Combinatorics</i>, vol. 29, no. 4, P4.13, The Electronic
    Journal of Combinatorics, 2022, doi:<a href="https://doi.org/10.37236/10794">10.37236/10794</a>.
  short: O. Cooley, M. Kang, J. Zalla, The Electronic Journal of Combinatorics 29
    (2022).
date_created: 2023-01-16T10:03:57Z
date_published: 2022-10-21T00:00:00Z
date_updated: 2023-08-04T10:29:18Z
day: '21'
ddc:
- '510'
department:
- _id: MaKw
doi: 10.37236/10794
external_id:
  isi:
  - '000876763300001'
file:
- access_level: open_access
  checksum: 00122b2459f09b5ae43073bfba565e94
  content_type: application/pdf
  creator: dernst
  date_created: 2023-01-30T11:45:13Z
  date_updated: 2023-01-30T11:45:13Z
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  file_name: 2022_ElecJournCombinatorics_Cooley_Kang_Zalla.pdf
  file_size: 626953
  relation: main_file
  success: 1
file_date_updated: 2023-01-30T11:45:13Z
has_accepted_license: '1'
intvolume: '        29'
isi: 1
issue: '4'
keyword:
- Computational Theory and Mathematics
- Geometry and Topology
- Theoretical Computer Science
- Applied Mathematics
- Discrete Mathematics and Combinatorics
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nd/4.0/
month: '10'
oa: 1
oa_version: Published Version
publication: The Electronic Journal of Combinatorics
publication_identifier:
  eissn:
  - 1077-8926
publication_status: published
publisher: The Electronic Journal of Combinatorics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Loose cores and cycles in random hypergraphs
tmp:
  image: /image/cc_by_nd.png
  legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode
  name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)
  short: CC BY-ND (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 29
year: '2022'
...