Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regular factors of regular graphs from eigenvalues   Let m and r be two integers. Let G be a connected r-regular graph of order n
and k an integer depending on m and r. For even kn, we find a best upper bound
(in terms of r and m) on the third largest eigenvalue that is sufficient to
guarantee that G has a k-factor. When nk is odd, we give a best upper bound (in
terms of r and m) on the second largest eigenvalue that is sufficient to
guarantee that G is k-critical.

23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs