# Hamiltonian Berge cycles in random hypergraphs

Deepak Bal, Ross Berkowitz, Pat Devlin, Mathias Schacht

Research output: Contribution to journalArticlepeer-review

## 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 Combinatorics Probability and Computing https://doi.org/10.1017/S0963548320000437 Accepted/In press - 2020

## Keywords

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