Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On curves intersecting at most once   We prove that on a closed surface of genus $g$, the cardinality of a set of
simple closed curves in which any two are non-homotopic and intersect at most
once is $\lesssim g^2 \log(g)$. This bound matches the largest known
constructions to within a logarithmic factor. The proof uses a probabilistic
argument in graph theory. It generalizes as well to the case of curves that
intersect at most $k$ times in pairs.

3
The categories of this paper are: physics
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org