Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Planar graphs without pairwise adjacent 3-,4-,5-, and 6-cycle are
  4-choosable   Xu and Wu proved that if every 5-cycle of a planar graph G is not
simultaneously adjacent to 3-cycles and 4-cycles, then G is 4-choosable. In
this paper, we improve this result as follows. If G is a planar graph without
pairwise adjacent 3-,4-,5-, and 6-cycle, then G is 4-choosable.

15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph