Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equitable Colorings of Corona Multiproducts of Graphs   A graph is equitably $k$-colorable if its vertices can be partitioned into
$k$ independent sets in such a way that the number of vertices in any two sets
differ by at most one. The smallest $k$ for which such a coloring exists is
known as the equitable chromatic number of $G$ and denoted $\chi_{=}(G)$. It is
known that this problem is NP-hard in general case and remains so for corona
graphs. In "Equitable colorings of Cartesian products of graphs" (2012) Lin and
Chang studied equitable coloring of Cartesian products of graphs. In this paper
we consider the same model of coloring in the case of corona products of
graphs. In particular, we obtain some results regarding the equitable chromatic
number for $l$-corona product $G \circ ^l H$, where $G$ is an equitably 3- or
4-colorable graph and $H$ is an $r$-partite graph, a path, a cycle or a
complete graph. Our proofs are constructive in that they lead to polynomial
algorithms for equitable coloring of such graph products provided that there is
given an equitable coloring of $G$. Moreover, we confirm Equitable Coloring
Conjecture for corona products of such graphs. This paper extends our results
from \cite{hf}.

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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph