Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Token Sliding on Chordal Graphs   Let I be an independent set of a graph G. Imagine that a token is located on
any vertex of I. We can now move the tokens of I along the edges of the graph
as long as the set of tokens still defines an independent set of G. Given two
independent sets I and J, the Token Sliding problem consists in deciding
whether there exists a sequence of independent sets which transforms I into J
so that every pair of consecutive independent sets of the sequence can be
obtained via a token move. This problem is known to be PSPACE-complete even on
planar graphs.
  In 2014, Demaine et al. asked whether the Token Sliding reconfiguration
problem is polynomial time solvable on interval graphs and more generally in
chordal graphs. Yamada and Uehara showed in 2016 that a polynomial time
transformation can be found in proper interval graphs.
  In this paper, we answer the first question of Demaine et al. and generalize
the result of Yamada and Uehara by showing that we can decide in polynomial
time whether two independent sets of an interval graph are in the same
connected component. Moveover, we answer similar questions by showing that: (i)
determining if there exists a token sliding transformation between every pair
of k-independent sets in an interval graph can be decided in polynomial time;
(ii) deciding this problem becomes co-NP-hard and even co-W[2]-hard
(parameterized by the size of the independent set) on split graphs, a sub-class
of chordal graphs.

4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: stat