Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower Bounds and properties for the average number of colors in the
  non-equivalent colorings of a graph   We study the average number $\mathcal{A}(G)$ of colors in the non-equivalent
colorings of a graph $G$. We show some general properties of this graph
invariant and determine its value for some classes of graphs. We then
conjecture several lower bounds on $\mathcal{A}(G)$ and prove that these
conjectures are true for specific classes of graphs such as triangulated graphs
and graphs with maximum degree at most 2.

28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th