Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The 3-colorability of planar graphs without cycles of length 4, 6 and 9   In this paper, we prove that planar graphs without cycles of length 4, 6, 9
are 3-colorable.

4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex