The threshold for the existence of Hamilton cycles in the random graph Gn,p has been known for many years, see [7], [1] and [3]. There have been many generalisations of these results over the years and the problem is well understood. It is natural to try to extend these results to Hypergraphs and this has proven to be difficult. The famous P´osa lemma fails to provide any comfort and we must seek new tools. In the graphical case, Hamilton cycles and perfect matchings go together and our approach will be to build on the deep and difficult result of Johansson, Kahn and Vu [6], as well as what we have learned from the graphical case.
