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- Title
Packing hamilton cycles in random and pseudo-random hypergraphs.
- Authors
Frieze, Alan; Krivelevich, Michael
- Abstract
We say that a k -uniform hypergraph C is a Hamilton cycle of type ℓ, for some 1 ≤ ℓ ≤ k, if there exists a cyclic ordering of the vertices of C such that every edge consists of k consecutive vertices and for every pair of consecutive edges E i-1, E i in C (in the natural ordering of the edges) we have | E i-1 / E i| = ℓ. We prove that for k/2 < ℓ ≤ k, with high probability almost all edges of the random k -uniform hypergraph H( n, p, k) with p( n) ≫ log 2 n/ n can be decomposed into edge-disjoint type ℓ Hamilton cycles. A slightly weaker result is given for ℓ = k/2. We also provide sufficient conditions for decomposing almost all edges of a pseudo-random k -uniform hypergraph into type ℓ Hamilton cycles, for k/2 ≤ ℓ ≤ k. For the case ℓ = k these results show that almost all edges of corresponding random and pseudo-random hypergraphs can be packed with disjoint perfect matchings. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012
- Publication
Random Structures & Algorithms, 2012, Vol 41, Issue 1, p1
- ISSN
1042-9832
- Publication type
Article
- DOI
10.1002/rsa.20396