Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complexity of tree-coloring interval graphs equitably   An equitable tree-$k$-coloring of a graph is a vertex $k$-coloring such that
each color class induces a forest and the size of any two color classes differ
by at most one. In this work, we show that every interval graph $G$ has an
equitable tree-$k$-coloring for any integer $k\geq
\lceil(\Delta(G)+1)/2\rceil$, solving a conjecture of Wu, Zhang and Li (2013)
for interval graphs, and furthermore, give a linear-time algorithm for
determining whether a proper interval graph admits an equitable
tree-$k$-coloring for a given integer $k$. For disjoint union of split graphs,
or $K_{1,r}$-free interval graphs with $r\geq 4$, we prove that it is
$W[1]$-hard to decide whether there is an equitable tree-$k$-coloring when
parameterized by number of colors, or by treewidth, number of colors and
maximum degree, respectively.

17
The categories of this paper are: q-fin
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The categories of this paper are: eess
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
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The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
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The categories of this paper are: econ
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: math-ph