Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rainbow fractional matchings   We prove that any family $E_1, \ldots , E_{\lceil rn \rceil}$ of (not
necessarily distinct) sets of edges in an $r$-uniform hypergraph, each having a
fractional matching of size $n$, has a rainbow fractional matching of size $n$
(that is, a set of edges from distinct $E_i$'s which supports such a fractional
matching). When the hypergraph is $r$-partite and $n$ is an integer, the number
of sets needed goes down from $rn$ to $rn-r+1$. The problem solved here is a
fractional version of the corresponding problem about rainbow matchings, which
was solved by Drisko and by Aharoni and Berger in the case of bipartite graphs,
but is open for general graphs as well as for $r$-partite hypergraphs with
$r>2$. Our topological proof is based on a result of Kalai and Meshulam about a
simplicial complex and a matroid on the same vertex set.

37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph