Packing tight Hamilton cycles in 3-uniform hypergraphs

Alan Frieze, Michael Krivelevich, Po Shen Loh

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Consider a 3-uniform hypergraph H 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 where every triple of consecutive vertices {vi,vi+1,vi+2} is an edge of C (indices considered modulo n). We develop new techniques which show 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, 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
Title of host publicationProceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011
PublisherAssociation for Computing Machinery
Pages913-932
Number of pages20
ISBN (Print)9780898719932
DOIs
StatePublished - 2011

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Fingerprint

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

Cite this