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