Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Packing Chromatic Number on Hamming Graphs and General Graphs   The packing chromatic number $\chi_\rho(G)$ of a graph $G$ is the smallest
integer $k$ needed to proper color the vertices of $G$ in such a way the
distance between any two vertices having color $i$ be at least $i+1$. We obtain
$\chi_\rho(H_{q,m})$ for $m=3$, where $H_{q,m}$ is the Hamming graph of words
of length $m$ and alphabet with $q$ symbols, and tabulate bounds of them for $m
\geq 4$ up to 10000 vertices. We also give a polynomial reduction from the
problem of finding $\chi_\rho(G)$ to the Maximum Stable Set problem.

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The categories of this paper are: quant-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th