Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a Cardinality-Constrained Transportation Problem With Market Choice   It is well-known that the intersection of the matching polytope with a
cardinality constraint is integral [8]. We prove a similar result for the
polytope corresponding to the transportation problem with market choice (TPMC)
(introduced in [4]) when the demands are in the set $\{1,2\}$. This result
generalizes the result regarding the matching polytope and also implies that
some special classes of minimum weight perfect matching problem with a
cardinality constraint on a subset of edges can be solved in polynomial time.

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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom