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Packing tight Hamilton cycles in 3-uniform hypergraphs

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journal contribution
posted on 01.12.2010, 00:00 by Alan Frieze, Michael Krivelevich, Po-Shen Loh

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.


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