### Abstract

We prove that certain collections of j-sets constructed during a breadth-first search process on j-components in a random k-uniform hypergraph are reasonably regularly distributed with high probability. We use this property to provide a short proof of the asymptotic size of the giant j-component shortly after it appears.

Original language | English |
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Article number | P3.6 |

Number of pages | 17 |

Journal | Electronic Journal of Combinatorics |

Volume | 26 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2019 |

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### Cite this

**The size of the giant component in random hypergraphs: A short proof.** / Cooley, O.; Kang, M.; Koch, C.

Research output: Contribution to journal › Article › Research › peer-review

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TY - JOUR

T1 - The size of the giant component in random hypergraphs: A short proof

AU - Cooley, O.

AU - Kang, M.

AU - Koch, C.

PY - 2019

Y1 - 2019

N2 - We consider connected components in k-uniform hypergraphs for the following notion of connectedness: given integers k≥2 and 1≤j≤k−1, two j-sets (of vertices) lie in the same j-component if there is a sequence of edges from one to the other such that consecutive edges intersect in at least j vertices.We prove that certain collections of j-sets constructed during a breadth-first search process on j-components in a random k-uniform hypergraph are reasonably regularly distributed with high probability. We use this property to provide a short proof of the asymptotic size of the giant j-component shortly after it appears.

AB - We consider connected components in k-uniform hypergraphs for the following notion of connectedness: given integers k≥2 and 1≤j≤k−1, two j-sets (of vertices) lie in the same j-component if there is a sequence of edges from one to the other such that consecutive edges intersect in at least j vertices.We prove that certain collections of j-sets constructed during a breadth-first search process on j-components in a random k-uniform hypergraph are reasonably regularly distributed with high probability. We use this property to provide a short proof of the asymptotic size of the giant j-component shortly after it appears.

UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85071910683&partnerID=MN8TOARS

U2 - https://www.combinatorics.org/ojs/index.php/eljc/article/view/v26i3p6/7863

DO - https://www.combinatorics.org/ojs/index.php/eljc/article/view/v26i3p6/7863

M3 - Article

VL - 26

JO - The electronic journal of combinatorics

JF - The electronic journal of combinatorics

SN - 1077-8926

IS - 3

M1 - P3.6

ER -