Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improving Lower Bounds for Equitable Chromatic Number   In many practical applications the underlying graph must be as equitable
colored as possible. A coloring is called equitable if the number of vertices
colored with each color differs by at most one, and the least number of colors
for which a graph has such a coloring is called its equitable chromatic number.
We introduce a new integer linear programming approach for studying the
equitable coloring number of a graph and show how to use it for improving lower
bounds for this number. The two stage method is based on finding or upper
bounding the maximum cardinality of an equitable color class in a valid
equitable coloring and, then, sequentially improving the lower bound for the
equitable coloring number. The computational experiments were carried out on
DIMACS graphs and other graphs from the literature.

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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph