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

O. Cooley, M. Kang, C. Koch

Research output: Contribution to journalArticleResearchpeer-review

Abstract

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.
Original languageEnglish
Article numberP3.6
Number of pages17
JournalElectronic Journal of Combinatorics
Volume26
Issue number3
DOIs
Publication statusPublished - 2019

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Giant Component
Hypergraph
Uniform Hypergraph
Breadth-first Search
Connectedness
Intersect
Connected Components
Consecutive
Integer

Cite this

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

In: Electronic Journal of Combinatorics, Vol. 26, No. 3, P3.6, 2019.

Research output: Contribution to journalArticleResearchpeer-review

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