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Independent Set Reconfiguration in Cographs

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Graph-Theoretic Concepts in Computer Science (WG 2014)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 8747))

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Abstract

We study the following independent set reconfiguration problem: 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 on \(n\) vertices, we show that it can be solved in polynomial time. More generally, we show that for a graph class \(\mathcal {G}\) that includes all chordal and claw-free graphs, the problem can be solved in polynomial time for graphs that can be obtained from a collection of graphs from \(\mathcal {G}\) using disjoint union and complete join operations.

Supported by the European Community’s Seventh Framework Programme (FP7/2007–2013), grant agreement n\(^{\circ }\) 317662.

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Authors and Affiliations

  1. Faculty of EEMCS, University of Twente, PO Box 217, 7500 AE, Enschede, The Netherlands

    Paul Bonsma

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  1. Paul Bonsma
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Correspondence to Paul Bonsma .

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Editors and Affiliations

  1. LITA, Université de Lorraine, Metz Cedex 01, France

    Dieter Kratsch

  2. Université d'Orléans, Orléans, France

    Ioan Todinca

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Bonsma, P. (2014). Independent Set Reconfiguration in Cographs. In: Kratsch, D., Todinca, I. (eds) Graph-Theoretic Concepts in Computer Science. WG 2014. Lecture Notes in Computer Science, vol 8747. Springer, Cham. https://doi.org/10.1007/978-3-319-12340-0_9

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  • DOI: https://doi.org/10.1007/978-3-319-12340-0_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12339-4

  • Online ISBN: 978-3-319-12340-0

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