Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Colorful Hamilton cycles in random graphs   Given an $n$ vertex graph whose edges have colored from one of $r$ colors
$C=\{c_1,c_2,\ldots,c_r\}$, we define the Hamilton cycle color profile $hcp(G)$
to be the set of vectors $(m_1,m_2,\ldots,m_r)\in [0,n]^r$ such that there
exists a Hamilton cycle that is the concatenation of $r$ paths
$P_1,P_2,\ldots,P_r$, where $P_i$ contains $m_i$ edges. We study $hcp(G_{n,p})$
when the edges are randomly colored. We discuss the profile close to the
threshold for the existence of a Hamilton cycle and the threshold for when
$hcp(G_{n,p})=\{(m_1,m_2,\ldots,m_r)\in [0,n]^r:m_1+m_2+\cdots+m_r=n\}$.

36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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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: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int