## Packing Hamilton Cycles in Random and Pseudo-Random Hypergraphs

#### journal contribution

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We say that a *k* -uniform hypergraph *C* is a Hamilton cycle of type *ℓ*, for some 1 ≤ *ℓ* ≤ *k*, if there exists a cyclic ordering of the vertices of *C*such that every edge consists of *k* consecutive vertices and for every pair of consecutive edges *E*_{i-1},*E*_{i} in *C* (in the natural ordering of the edges) we have |*E*_{i-1} / *E*_{i}| = *ℓ*. We prove that for *k*/2 < *ℓ* ≤ *k*, with high probability almost all edges of the random *k* -uniform hypergraph*H*(*n*,*p*,*k*) with *p*(*n*) ≫ log ^{2}*n*/*n* can be decomposed into edge-disjoint type *ℓ* Hamilton cycles. A slightly weaker result is given for *ℓ* = *k*/2. We also provide sufficient conditions for decomposing almost all edges of a pseudo-random *k* -uniform hypergraph into type *ℓ* Hamilton cycles, for *k*/2 ≤ *ℓ* ≤ *k*. For the case *ℓ* = *k* these results show that almost all edges of corresponding random and pseudo-random hypergraphs can be packed with disjoint perfect matchings.