2015/02/25 by Oliver Cooley, Cooley, Oliver, Mihyun Kang +3
Mathematics · Physics and Astronomy · #05C65 #05C80 #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #math.CO #msc:05C65 #msc:05C80
paper · pdf · doi:10.48550/arxiv.1502.07289
10 pages
arxiv created 2015/02/25 · openalex publication_date 2015/02/25 · arxiv updated 2015/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the following definition of connectivity in k-uniform hypergraphs: Two j-sets are j-connected if there is a walk of edges between them such that two consecutive edges intersect in at least j vertices. 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 well-known results for graphs.