Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cubic graphs with small independence ratio   Let $i(r,g)$ denote the infimum of the ratio $\frac{\alpha(G)}{|V(G)|}$ over
the $r$-regular graphs of girth at least $g$, where $\alpha(G)$ is the
independence number of $G$, and let $i(r,\infty) := \lim\limits_{g \to \infty}
i(r,g)$. Recently, several new lower bounds of $i(3,\infty)$ were obtained. In
particular, Hoppen and Wormald showed in 2015 that $i(3, \infty) \ge 0.4375$,
and Cs\'oka improved it to $i(3,\infty) \ge 0.44533$ in 2016. Bollob\'as proved
the upper bound $i(3,\infty) < \frac{6}{13}$ in 1981, and McKay improved it to
$i(3,\infty) < 0.45537$ in 1987. There were no improvements since then. In this
paper, we improve the upper bound to $i(3,\infty) \le 0.454.$

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The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio