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On the Relation of Strong Triadic Closure and Cluster Deletion

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Graph-Theoretic Concepts in Computer Science (WG 2018)

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Abstract

We study the parameterized and classical complexity of two related problems on undirected graphs \(G=(V,E)\). In Strong Triadic Closure we aim to label the edges in E as strong and weak such that at most k edges are weak and G contains no induced \(P_3\) with two strong edges. In Cluster Deletion we aim to destroy all induced \(P_3\)s by a minimum number of edge deletions. We first show that Strong Triadic Closure admits a 4k-vertex kernel. Then, we study parameterization by \(\ell :=|E|-k\) and show that both problems are fixed-parameter tractable and unlikely to admit a polynomial kernel with respect to \(\ell \). Finally, we give a dichotomy of the classical complexity of both problems on H-free graphs for all H of order four.

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Authors and Affiliations

  1. Fachbereich für Mathematik und Informatik, Philipps-Universität Marburg, Marburg, Germany

    Niels Grüttemeier & Christian Komusiewicz

Authors
  1. Niels Grüttemeier
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  2. Christian Komusiewicz
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Correspondence to Niels Grüttemeier .

Editor information

Editors and Affiliations

  1. Universität Rostock, Rostock, Germany

    Andreas Brandstädt

  2. Brandenburgische Technische Universität Cottbus-Senftenberg, Cottbus, Germany

    Ekkehard Köhler

  3. Brandenburgische Technische Universität Cottbus-Senftenberg, Cottbus, Germany

    Klaus Meer

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Grüttemeier, N., Komusiewicz, C. (2018). On the Relation of Strong Triadic Closure and Cluster Deletion. In: Brandstädt, A., Köhler, E., Meer, K. (eds) Graph-Theoretic Concepts in Computer Science. WG 2018. Lecture Notes in Computer Science(), vol 11159. Springer, Cham. https://doi.org/10.1007/978-3-030-00256-5_20

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  • DOI: https://doi.org/10.1007/978-3-030-00256-5_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00255-8

  • Online ISBN: 978-3-030-00256-5

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