Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Loose Hamilton Cycles in Random Uniform Hypergraphs   In the random hypergraph $H_{n,p;k}$ each possible $k$-tuple appears
independently with probability $p$. A loose Hamilton cycle is a cycle 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 $$\lim_{\substack{n\to \infty
2(k-1) |n}}\Pr(H_{n,p;k}\ contains\ a\ loose\ Hamilton\ cycle)=1.$$ This is
asymptotically best possible.

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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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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: hep-th
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The categories of this paper are: hep-ph