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Token Jumping in Minor-Closed Classes

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Fundamentals of Computation Theory (FCT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10472))

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Abstract

Given two k-independent sets I and J of a graph G, one can ask if it is possible to transform the one into the other in such a way that, at any step, we replace one vertex of the current independent set by another while keeping the property of being independent. Deciding this problem, known as the Token Jumping (TJ) reconfiguration problem, is PSPACE-complete even on planar graphs. Ito et al. proved in 2014 that the problem is FPT parameterized by k if the input graph is \(K_{3,\ell }\)-free.

We prove that the result of Ito et al. can be extended to any \(K_{\ell ,\ell }\)-free graphs. In other words, if G is a \(K_{\ell ,\ell }\)-free graph, then it is possible to decide in FPT-time if I can be transformed into J. As a by product, the TJ-reconfiguration problem is FPT in many well-known classes of graphs such as any minor-free class.

N. Bousquet—The author is partially supported by ANR project STINT (ANR-13-BS02-0007).

A. Mary—The author is partially supported by ANR project GraphEn (ANR-15-CE40-0009).

A. Parreau—The author is partially supported by ANR project GAG (ANR-14-CE25-0006).

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Notes

  1. 1.

    Under standard algorithmic assumptions, W[1]-hard problems do not admit FPT algorithms.

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Authors and Affiliations

  1. Laboratoire G-SCOP, CNRS, Univ. Grenoble Alpes, Grenoble, France

    Nicolas Bousquet

  2. Univ Lyon, Université Lyon 1, LBBE CNRS UMR 5558, 69622, Lyon, France

    Arnaud Mary

  3. Univ Lyon, Université Lyon 1, LIRIS UMR CNRS 5205, 69621, Lyon, France

    Aline Parreau

Authors
  1. Nicolas Bousquet
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  2. Arnaud Mary
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  3. Aline Parreau
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Correspondence to Nicolas Bousquet .

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Editors and Affiliations

  1. CNRS, University of Bordeaux, Talence cedex, France

    Ralf Klasing

  2. LaBRI, University of Bordeaux, Talence cedex, France

    Marc Zeitoun

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Bousquet, N., Mary, A., Parreau, A. (2017). Token Jumping in Minor-Closed Classes. In: Klasing, R., Zeitoun, M. (eds) Fundamentals of Computation Theory. FCT 2017. Lecture Notes in Computer Science(), vol 10472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55751-8_12

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  • DOI: https://doi.org/10.1007/978-3-662-55751-8_12

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