Hamiltonian cycles in hypergraphs

In this note, we study the emergence of Hamiltonian Berge cycles in random $r$-uniform hypergraphs.  In particular, we show that for $r \geq 3$ the $2$-out random $r$-graph almost surely has such a cycle, and we use this to determine (up to a multiplicative factor) the threshold probability for when the Erdős–Rényi random $r$-graph is likely to have such a cycle. In particular, in the Erdős–Rényi model we show (up to a constant factor depending on $r$) the emergence of these cycles essentially coincides with the disappearance of vertices of degree at most $2$.  This is a joint work with Deepak Bal.