## Abstract

In this note we study the emergence of Hamiltonian Berge cycles in random r-uniform hypergraphs. For <![CDATA[ $r\geq 3$ ]]> 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 Erd '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 language | English |
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Journal | Combinatorics Probability and Computing |

DOIs | |

State | Accepted/In press - 2020 |

## Keywords

- 05C20
- 05C38
- 05C45
- 05C65
- 05C80
- 05D40
- 2020 MSC Codes: