Loose Hamilton Cycles in Random 3-Uniform Hypergraphs

Details Loose Hamilton Cycles in Random 3-Uniform Hypergraphs Loose Hamilton Cycles in Random 3-Uniform Hypergraphs

2010-03-30

arxiv.org/abs/1003.5817v1

Mathematics

Combinatorics

4 pages

Scientific paper

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.

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