Packing tight Hamilton cycles in 3-uniform hypergraphs
Let H be a 3-uniform hypergraph with n vertices. A tight Hamilton cycle C ? H is a collection of n edges for which there is an ordering of the vertices v1,,vn such that every triple of consecutive vertices {vi,vi+1,vi+2} is an edge of C (indices are considered modulo n ). We develop new techniques which enable us to prove that under certain natural pseudo-random conditions, almost all edges of H can be covered by edge-disjoint tight Hamilton cycles, for n divisible by 4. Consequently, we derive the corollary that random 3-uniform hypergraphs can be almost completely packed with tight Hamilton cycles whp, for n divisible by 4 and p not too small. Along the way, we develop a similar result for packing Hamilton cycles in pseudo-random digraphs with even numbers of vertices.  2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011
packing hamilton cycles random hypergraphs