Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Holt-Klee Property for Oriented Matroid Programming   The Holt-Klee theorem says that the graph of a $d$-polytope, with edges
oriented by a linear function on $P$ that is not constant on any edge, admits
$d$ independent monotone paths from the source to the sink. We prove that the
digraphs obtained from oriented matroid programs of rank $d+1$ on $n+2$
elements, which include those from $d$-polytopes with $n$ facets, admit $d$
independent monotone paths from source to sink if $d \le 4$. This was
previously only known to hold for $d\le 3$ and $n\le 6$.

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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph