Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An approximate version of a conjecture of Aharoni and Berger   Aharoni and Berger conjectured that in every proper edge-colouring of a
bipartite multigraph by $n$ colours with at least $n+1$ edges of each colour
there is a rainbow matching using every colour. This conjecture generalizes a
longstanding problem of Brualdi and Stein about transversals in Latin squares.
Here an approximate version of the Aharoni-Berger Conjecture is proved---it is
shown that if there are at least $n+o(n)$ edges of each colour in a proper
$n$-edge-colouring of a bipartite multigraph then there is a rainbow matching
using every colour.

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The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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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: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom