Threshold and Hitting Time for High-order Connectivity in Random Hypergraphs Oliver Cooley, Mihyun Kang and Christoph Koch
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چکیده
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.
منابع مشابه
Threshold and Hitting Time for High-Order Connectedness in Random Hypergraphs
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 jconnected if all j-sets are pairwise j-connected. We determine the threshold at which the random k-uniform hypergraph with edge probability p b...
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تاریخ انتشار 2015