Tight Hamilton Cycles in Random Uniform Hypergraphs

<p>In this paper we show that <em>e</em>/<em>n</em> is the sharp threshold for the existence of tight Hamilton cycles in random <em>k</em> -uniform hypergraphs, for all <em>k</em> ≥ 4. When <em>k</em> = 3 we show that 1/<em>n</em> is an asymptotic threshold. We also determine thresholds for the existence of other types of Hamilton cycles.</p>