Hamiltonian Berge cycles in random hypergraphs

Deepak Bal, Ross Berkowitz, Pat Devlin, Mathias Schacht

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this note we study the emergence of Hamiltonian Berge cycles in random r-uniform hypergraphs. For we prove an optimal stopping time result that if edges are sequentially added to an initially empty r-graph, then as soon as the minimum degree is at least 2, the hypergraph with high probability has such a cycle. In particular, this determines the threshold probability for Berge Hamiltonicity of the ErdÅ s-Rényi random r-graph, and we also show that the 2-out random r-graph with high probability has such a cycle. We obtain similar results for weak Berge cycles as well, thus resolving a conjecture of Poole.

Original languageEnglish
Pages (from-to)228-238
Number of pages11
JournalCombinatorics Probability and Computing
Volume30
Issue number2
DOIs
StatePublished - Mar 2021

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