Loose Cores and Cycles in Random Hypergraphs

Oliver Cooley, Mihyun Kang, Julian Zalla*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


The loose core in hypergraphs is a structure inspired by loose cycles which mirrors the close relationship between 2-cores and cycles in graphs. We prove that the order of the loose core undergoes a phase transition at a certain critical threshold in the r-uniform binomial random hypergraph Hr(n, p) for every r≥ 3. We also determine the asymptotic number of vertices and edges in the loose core of Hr(n, p). Furthermore we obtain an improved upper bound on the length of the longest loose cycle in Hr(n, p).

Original languageEnglish
Title of host publicationTrends in Mathematics
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages6
Publication statusPublished - 2021

Publication series

NameTrends in Mathematics
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X


  • Factor graphs
  • Loose cores
  • Loose cycles
  • Peeling processes
  • Random hypergraphs

ASJC Scopus subject areas

  • Mathematics(all)

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