Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three-coloring graphs with no induced seven-vertex path I : the
  triangle-free case   In this paper, we give a polynomial time algorithm which determines if a
given triangle-free graph with no induced seven-vertex path is 3-colorable, and
gives an explicit coloring if one exists.

34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int