10.1184/R1/6479093.v1 Alan Frieze Alan Frieze Michael Krivelevich Michael Krivelevich Po-Shen Loh Po-Shen Loh Packing tight Hamilton cycles in 3-uniform hypergraphs Carnegie Mellon University 2010 Mathematical Sciences 2010-12-01 00:00:00 Journal contribution https://kilthub.cmu.edu/articles/journal_contribution/Packing_tight_Hamilton_cycles_in_3-uniform_hypergraphs/6479093 <p>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.</p>