Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On triangle-free graphs that do not contain a subdivision of the
  complete graph on four vertices as an induced subgraph   We prove a decomposition theorem for the class of triangle-free graphs that
do not contain a subdivision of the complete graph on four vertices as an
induced subgraph. We prove that every graph of girth at least~5 in this class
is 3-colorable.

15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org