Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Short Proof of the Toughness of Delaunay Triangulations   We present a self-contained short proof of the seminal result of Dillencourt
(SoCG 1987 and DCG 1990) that Delaunay triangulations, of planar point sets in
general position, are 1-tough. An important implication of this result is that
Delaunay triangulations have perfect matchings. Another implication of our
result is a proof of the conjecture of Aichholzer et al. (2010) that at least
$n$ points are required to block any $n$-vertex Delaunay triangulation

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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con