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

  • Daniël Paulusma
  • Christophe Picouleau
  • Bernard RiesEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10185)


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.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Daniël Paulusma
    • 1
  • Christophe Picouleau
    • 2
  • Bernard Ries
    • 3
    Email author
  1. 1.Durham UniversityDurhamUK
  2. 2.CNAM, Laboratoire CEDRICParisFrance
  3. 3.University of FribourgFribourgSwitzerland

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