Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Alon-Tarsi number of planar graphs without cycles of lengths $4$ and
  $l$   This paper proves that if $G$ is a planar graph without 4-cycles and
$l$-cycles for some $l\in\{5, 6, 7\}$, then there exists a matching $M$ such
that $AT(G-M)\leq 3$. This implies that every planar graph without 4-cycles and
$l$-cycles for some $l\in\{5, 6, 7\}$ is 1-defective 3-paintable.

37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn