## 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 language | English |
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Pages (from-to) | 269-300 |

Number of pages | 32 |

Journal | Random Structures and Algorithms |

Volume | 40 |

Issue number | 3 |

DOIs | |

State | Published - May 2012 |

## Keywords

- Hamilton cycles
- Packing
- Random hypergraphs