Loose Hamilton cycles in random 3-uniform hypergraphs
The electronic journal of combinatorics, Tome 17 (2010)
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 $i=1,2,\ldots,n/2$ where $x_1,x_2,\ldots,x_{n/2},y_1,y_2,\ldots,y_{n/2}$ are all distinct. We prove that there exists an absolute constant $K>0$ such that if $p\geq {K\log n\over n^2}$ then $$\lim_{\textstyle{n\to \infty\atop 4|n}}\Pr(H_{n,p;3}\ contains\ a\ loose\ Hamilton\ cycle)=1.$$
@article{10_37236_477,
author = {Alan Frieze},
title = {Loose {Hamilton} cycles in random 3-uniform hypergraphs},
journal = {The electronic journal of combinatorics},
year = {2010},
volume = {17},
doi = {10.37236/477},
zbl = {1189.05117},
url = {http://geodesic.mathdoc.fr/articles/10.37236/477/}
}
Alan Frieze. Loose Hamilton cycles in random 3-uniform hypergraphs. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/477
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