Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: De Bruijn-Erd\H{o}s type theorems for graphs and posets   A classical theorem of De Bruijn and Erd\H{o}s asserts that any noncollinear
set of n points in the plane determines at least n distinct lines. We prove
that an analogue of this theorem holds for graphs. Restricting our attention to
comparability graphs, we obtain a version of the De Bruijn-Erd\H{o}s theorem
for partially ordered sets (posets). Moreover, in this case, we have an
improved bound on the number of lines depending on the height of the poset. The
extremal configurations are also determined.

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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg