Geodesic
Loose Hamilton cycles in random uniform hypergraphs
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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In the random $k$-uniform hypergraph $H_{n,p;k}$ of order $n$ each possible $k$-tuple appears independently with probability $p$. A loose Hamilton cycle is a cycle of order $n$ in which every pair of adjacent edges intersects in a single vertex. We prove that if $p n^{k-1}/\log n$ tends to infinity with $n$ then $$\lim_{\substack{n\to \infty\\ 2(k-1) |n}}\Pr(H_{n,p;k}\text{ contains a loose Hamilton cycle})=1.$$ This is asymptotically best possible.
DOI : 10.37236/535
Classification : 05C80, 05C45, 05C38, 05C65 
@article{10_37236_535,
     author = {Andrzej Dudek and Alan Frieze},
     title = {Loose {Hamilton} cycles in random uniform hypergraphs},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/535},
     zbl = {1218.05174},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/535/}
}
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Andrzej Dudek; Alan Frieze. Loose Hamilton cycles in random uniform hypergraphs. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/535

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