Packing tight Hamilton cycles in 3-uniform hypergraphs

Alan Frieze, Michael Krivelevich, Po Shen Loh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)269-300
Number of pages32
JournalRandom Structures and Algorithms
Volume40
Issue number3
DOIs
StatePublished - May 2012

Keywords

  • Hamilton cycles
  • Packing
  • Random hypergraphs

Fingerprint

Dive into the research topics of 'Packing tight Hamilton cycles in 3-uniform hypergraphs'. Together they form a unique fingerprint.

Cite this