TY - GEN

T1 - Packing tight Hamilton cycles in 3-uniform hypergraphs

AU - Frieze, Alan

AU - Krivelevich, Michael

AU - Loh, Po Shen

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79955726673&partnerID=8YFLogxK

U2 - 10.1137/1.9781611973082.71

DO - 10.1137/1.9781611973082.71

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AN - SCOPUS:79955726673

SN - 9780898719932

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 913

EP - 932

BT - Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011

PB - Association for Computing Machinery

ER -