English

Loose Hamilton Cycles in Random 3-Uniform Hypergraphs

Combinatorics 2010-03-31 v1

Abstract

In the random hypergraph H=H(n,p;3) each possible triple appears independently with probability p. A loose Hamilton cycle can be described as a sequence of edges {x_i,y_i,x_{i+1}\} for i=1,2,...,n/2. We prove that there exists an absolute constant K>0 such that if p>K\log n/n^2 then lim_{n->oo 4 |n}}Pr(H(n,p;3) contains a loose Hamilton cycle)=1.

Keywords

Cite

@article{arxiv.1003.5817,
  title  = {Loose Hamilton Cycles in Random 3-Uniform Hypergraphs},
  author = {Alan Frieze},
  journal= {arXiv preprint arXiv:1003.5817},
  year   = {2010}
}

Comments

4 pages

R2 v1 2026-06-21T15:04:30.662Z