Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Construction of $k$-matchings and $k$-regular subgraphs in graph
  products
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess