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 v 1 ,…, v n such that every triple of consecutive vertices { v i , v i +1 , v i +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