Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A generalization of hall's theorem for k-uniform k-partite hypergraphs   In this paper we prove a generalized version of Hall's theorem for
hypergraphs. More precisely, let H be a k-uniform k- partite hypergraph with
some ordering on parts as V1, V2,..., Vk. such that the subhypergraph generated
on union of V1, V2,..., Vk-1 has a unique perfect matching. In this case, we
give a necessary and sufficient condition for having a matching of size t =
|V1| in H. Some relevant results and counterexamples are given as well.

35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc