Packing tight Hamilton cycles in 3-uniform hypergraphs

Consider a 3-uniform hypergraph <i>H</i> with <i>n</i> vertices. A tight Hamilton cycle <i>C</i> ⊂ <i>H</i> is a collection of <i>n</i> edges for which there is an ordering of the vertices <i>v</i><sub>1</sub>,..., <i>v</i><sub><i>n</i></sub> where every triple of consecutive vertices {<i>v</i><sub><i>i</i></sub>, <i>v</i><sub><i>i</i>+1</sub>, <i>v</i><sub><i>i</i>+2</sub>} is an edge of <i>C</i> (indices considered modulo <i>n</i>). We develop new techniques which show that under certain natural pseudo-random conditions, almost all edges of <i>H</i> can be covered by edge-disjoint tight Hamilton cycles, for <i>n</i> divisible by 4. Consequently, random 3-uniform hypergraphs can be almost completely packed with tight Hamilton cycles <b>whp</b>, for <i>n</i> divisible by 4 and <i>p</i> not too small. Along the way, we develop a similar result for packing Hamilton cycles in pseudo-random digraphs with even numbers of vertices.

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