Loose Cores and Cycles in Random Hypergraphs

Oliver Cooley; Mihyun Kang; Julian Zalla

doi:10.1007/978-3-030-83823-2_44

Loose Cores and Cycles in Random Hypergraphs

Oliver Cooley, Mihyun Kang, Julian Zalla^*

^*Corresponding author for this work

Institute of Discrete Mathematics (5050)

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

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 H^r(n, p) for every r≥ 3. We also determine the asymptotic number of vertices and edges in the loose core of H^r(n, p). Furthermore we obtain an improved upper bound on the length of the longest loose cycle in H^r(n, p).

Original language	English
Title of host publication	Trends in Mathematics
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	280-285
Number of pages	6
DOIs	https://doi.org/10.1007/978-3-030-83823-2_44
Publication status	Published - 2021

Publication series

Name	Trends in Mathematics
Volume	14
ISSN (Print)	2297-0215
ISSN (Electronic)	2297-024X

Keywords

Factor graphs
Loose cores
Loose cycles
Peeling processes
Random hypergraphs

ASJC Scopus subject areas

General Mathematics

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10.1007/978-3-030-83823-2_44

Cite this

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AU - Kang, Mihyun

AU - Zalla, Julian

PY - 2021

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AB - 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).

KW - Factor graphs

KW - Loose cores

KW - Loose cycles

KW - Peeling processes

KW - Random hypergraphs

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M3 - Chapter

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EP - 285

BT - Trends in Mathematics

PB - Springer Science and Business Media Deutschland GmbH

ER -

Loose Cores and Cycles in Random Hypergraphs

Abstract

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Keywords

ASJC Scopus subject areas

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