---
res:
bibo_abstract:
- "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 $H^r(n,p)$.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Oliver
foaf_name: Cooley, Oliver
foaf_surname: Cooley
foaf_workInfoHomepage: http://www.librecat.org/personId=43f4ddd0-a46b-11ec-8df6-ef3703bd721d
- foaf_Person:
foaf_givenName: Mihyun
foaf_name: Kang, Mihyun
foaf_surname: Kang
- foaf_Person:
foaf_givenName: Julian
foaf_name: Zalla, Julian
foaf_surname: Zalla
bibo_doi: 10.37236/10794
bibo_issue: '4'
bibo_volume: 29
dct_date: 2022^xs_gYear
dct_identifier:
- UT:000876763300001
dct_isPartOf:
- http://id.crossref.org/issn/1077-8926
dct_language: eng
dct_publisher: The Electronic Journal of Combinatorics@
dct_subject:
- Computational Theory and Mathematics
- Geometry and Topology
- Theoretical Computer Science
- Applied Mathematics
- Discrete Mathematics and Combinatorics
dct_title: Loose cores and cycles in random hypergraphs@
...