Threshold and hitting time for high-order connectedness in random hypergraphs

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We consider the following definition of connectedness in k-uniform hypergraphs: two j-sets (sets of j vertices) are j-connected if there is a walk of edges between them such that two consecutive edges intersect in at least j vertices. The hypergraph is j-connected if all j-sets are pairwise j-connected. We determine the threshold at which the random k-uniform hypergraph with edge probability p becomes j-connected with high probability. We also deduce a hitting time result for the random hypergraph process – the hypergraph becomes j-connected at exactly the moment when the last isolated j-set disappears. This generalises the classical hitting time result of Bollobás and Thomason for graphs.
Original languageEnglish
Article numberP2.48
Number of pages14
JournalThe Electronic Journal of Combinatorics
Issue number2
Publication statusPublished - 10 Jun 2016

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)


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