Loose Cores and Cycles in Random Hypergraphs

@inproceedings{Cooley2021LooseCA,
  title={Loose Cores and Cycles in Random Hypergraphs},
  author={Oliver Cooley and Mihyun Kang and Julian Zalla},
  year={2021}
}
Inspired by the study of loose cycles in hypergraphs, we define the loose core in hypergraphs as a structure which mirrors the close relationship between cycles and 2-cores in graphs. We prove that in the r-uniform binomial random hypergraph H(n, p), the order of the loose core undergoes a phase transition at a certain critical threshold and determine this order, as well as the number of edges, asymptotically in the subcritical and supercritical regimes. Our main tool is an algorithm called… 
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