Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three-coloring triangle-free graphs on surfaces III. Graphs of girth
  five   We show that the size of a 4-critical graph of girth at least five is bounded
by a linear function of its genus. This strengthens the previous bound on the
size of such graphs given by Thomassen. It also serves as the basic case for
the description of the structure of 4-critical triangle-free graphs embedded in
a fixed surface, presented in a future paper of this series.

17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg