Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: On the existence and number of $(k+1)$-kings in $k$-quasi-transitive
  digraphs
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga