Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The upper bound on number of graphs, with fixed number of vertices, that
  vertices can be colored with n colors   In the paper we state and prove theorem describing the upper bound on number
of the graphs that have fixed number of vertices |V| and can be colored with
the fixed number of n colors. The bound relates both numbers using power of 2,
while the exponent is the difference between |V| and n. We also state three
conjectures on the number of graphs that have fixed number of vertices |V| and
chromatic number n.

17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph