Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact minimum degree thresholds for perfect matchings in uniform
  hypergraphs   Given positive integers k and r where 4 divides k and k/2 \leq r \leq k-1, we
give a minimum r-degree condition that ensures a perfect matching in a
k-uniform hypergraph. This condition is best possible and improves on work of
Pikhurko who gave an asymptotically exact result. Our approach makes use of the
absorbing method, as well as the hypergraph removal lemma and a structural
result of Keevash and Sudakov relating to the Turan number of the expanded
triangle.

13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin