Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Independent Set Reconfiguration in Cographs   We study the following independent set reconfiguration problem, called
TAR-Reachability: given two independent sets $I$ and $J$ of a graph $G$, both
of size at least $k$, is it possible to transform $I$ into $J$ by adding and
removing vertices one-by-one, while maintaining an independent set of size at
least $k$ throughout? This problem is known to be PSPACE-hard in general. For
the case that $G$ is a cograph (i.e. $P_4$-free graph) on $n$ vertices, we show
that it can be solved in time $O(n^2)$, and that the length of a shortest
reconfiguration sequence from $I$ to $J$ is bounded by $4n-2k$, if such a
sequence exists.
  More generally, we show that if $X$ is a graph class for which (i)
TAR-Reachability can be solved efficiently, (ii) maximum independent sets can
be computed efficiently, and which satisfies a certain additional property,
then the problem can be solved efficiently for any graph that can be obtained
from a collection of graphs in $X$ using disjoint union and complete join
operations. Chordal graphs are given as an example of such a class $X$.

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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol