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International Conference on Theory and Applications of Models of Computation

TAMC 2017: Theory and Applications of Models of Computation pp 470–483Cite as

Blocking Independent Sets for H-Free Graphs via Edge Contractions and Vertex Deletions

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 10185)

Abstract

Let d and k be two given integers, and let G be a graph. Can we reduce the independence number of G by at least d via at most k graph operations from some fixed set S? This problem belongs to a class of so-called blocker problems. It is known to be co-NP-hard even if S consists of either an edge contraction or a vertex deletion. We further investigate its computational complexity under these two settings:

  • we give a sufficient condition on a graph class for the vertex deletion variant to be co-NP-hard even if \(d=k=1\);

  • in addition we prove that the vertex deletion variant is co-NP-hard for triangle-free graphs even if \(d=k=1\);

  • we prove that the edge contraction variant is NP-hard for bipartite graphs but linear-time solvable for trees.

By combining our new results with known ones we are able to give full complexity classifications for both variants restricted to H-free graphs.

D. Paulusma received support from EPSRC (EP/K025090/1).

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Author information

Authors and Affiliations

  1. Durham University, Durham, UK

    Daniël Paulusma

  2. CNAM, Laboratoire CEDRIC, Paris, France

    Christophe Picouleau

  3. University of Fribourg, Fribourg, Switzerland

    Bernard Ries

Authors
  1. Daniël Paulusma
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  2. Christophe Picouleau
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  3. Bernard Ries
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Corresponding author

Correspondence to Bernard Ries .

Editor information

Editors and Affiliations

  1. Anna University, Chennai, India

    T.V. Gopal

  2. Universität Bern , Bern, Switzerland

    Gerhard Jäger

  3. Universität Bern , Bern, Switzerland

    Silvia Steila

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Paulusma, D., Picouleau, C., Ries, B. (2017). Blocking Independent Sets for H-Free Graphs via Edge Contractions and Vertex Deletions. In: Gopal, T., Jäger , G., Steila, S. (eds) Theory and Applications of Models of Computation. TAMC 2017. Lecture Notes in Computer Science(), vol 10185. Springer, Cham. https://doi.org/10.1007/978-3-319-55911-7_34

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  • DOI: https://doi.org/10.1007/978-3-319-55911-7_34

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