Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An improved bound on the sizes of matchings guaranteeing a rainbow
  matching   A conjecture by Aharoni and Berger states that every family of $n$ matchings
of size $n+1$ in a bipartite multigraph contains a rainbow matching of size
$n$. In this paper we prove that matching sizes of $(3/2 + o(1)) n$ suffice to
guarantee such a rainbow matching, which is asymptotically the same bound as
the best known one in case we only aim to find a rainbow matching of size
$n-1$. This improves previous results by Aharoni, Charbit and Howard, and
Kotlar and Ziv.

24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc