Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Loose Hamilton Cycles in Random 3-Uniform Hypergraphs   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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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph