Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pattern Colored Hamilton Cycles in Random Graphs   We consider the existence of patterned Hamilton cycles in randomly colored
random graphs. Given a string $\Pi$ over a set of colors $\{1,2,\ldots,r\}$, we
say that a Hamilton cycle is $\Pi$-colored if the pattern repeats at intervals
of length $|\Pi|$ as we go around the cycle. We prove a hitting time for the
existence of such a cycle. We also prove a hitting time result for a related
notion of $\Pi$-connected.

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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci