Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: On degree sum conditions for 2-factors with a prescribed number of
  cycles
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio