Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The k-planar crossing number of random graphs and random regular graphs   We give an explicit extension of Spencer's result on the biplanar crossing
number of the Erdos-Renyi random graph $G(n,p)$. In particular, we show that
the k-planar crossing number of $G(n,p)$ is almost surely $\Omega((n^2p)^2)$.
Along the same lines, we prove that for any fixed $k$, the $k$-planar crossing
number of various models of random $d$-regular graphs is $\Omega ((dn)^2)$ for
$d > c_0$ for some constant $c_0=c_0(k)$.

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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con