Tight Hamilton Cycles in Random Uniform Hypergraphs
  In this paper we show that $e/n$ is the sharp threshold for the existence of tight Hamilton cycles in random $k$-uniform hypergraphs, for all $k\ge 4$. When $k=3$ we show that $1/n$ is an asymptotic threshold. We also determine thresholds for the existence of other types of Hamilton cycles. 
Andrzej Dudek, Alan Frieze
math.CO