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We say that a $k$-uniform hypergraph $C$ is a Hamilton cycle of type $\ell$,for some $1\le \ell \le k$, if there exists a cyclic ordering of the verticesof $C$ such that every edge consists of $k$ consecutive vertices and for everypair of consecutive edges $E_{i-1},E_i$ in $C$ (in the natural ordering of theedges) we have $|E_{i-1}-E_i|=\ell$. We prove that for $\ell \le k\le 2\ell$,with high probability almost all edges of a random $k$-uniform hypergraph$H(n,p,k)$ with $p(n)\gg \log^2 n/n$ can be decomposed into edge disjoint type$\ell$ Hamilton cycles. We also provide sufficient conditions for decomposingalmost all edges of a pseudo-random $k$-uniform hypergraph into type $\ell$Hamilton cycles, for $\ell \le k\le 2\ell$. For the case $\ell=k$ these resultsshow that almost all edges of corresponding random and pseudo-randomhypergraphs can be packed into disjoint perfect matchings.

Packing Hamilton Cycles in Random and Pseudo-Random Hypergraphs