Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parameterized Complexity of Equitable Coloring   A graph on $n$ vertices is equitably $k$-colorable if it is $k$-colorable and
every color is used either $\left\lfloor n/k \right\rfloor$ or $\left\lceil n/k
\right\rceil$ times.
  Such a problem appears to be considerably harder than vertex coloring, being
$\mathsf{NP\text{-}Complete}$ even for cographs and interval graphs.
  In this work, we prove that it is $\mathsf{W[1]\text{-}Hard}$ for block
graphs and for disjoint union of split graphs when parameterized by the number
of colors; and $\mathsf{W[1]\text{-}Hard}$ for $K_{1,4}$-free interval graphs
when parameterized by treewidth, number of colors and maximum degree,
generalizing a result by Fellows et al. (2014) through a much simpler
reduction.
  Using a previous result due to Dominique de Werra (1985), we establish a
dichotomy for the complexity of equitable coloring of chordal graphs based on
the size of the largest induced star.
  Finally, we show that \textsc{equitable coloring} is $\mathsf{FPT}$ when
parameterized by the treewidth of the complement graph.

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The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph