On the Parameterized Complexity of Cutting a Few Vertices from a Graph

  • Fedor V. Fomin
  • Petr A. Golovach
  • Janne H. Korhonen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8087)


We study the parameterized complexity of separating a small set of vertices from a graph by a small vertex-separator. That is, given a graph G and integers k, t, the task is to find a vertex set X with |X| ≤ k and |N(X)| ≤ t. We show that
  • the problem is fixed-parameter tractable (FPT) when parameterized by t but W[1]-hard when parameterized by k, and

  • a terminal variant of the problem, where X must contain a given vertex s, is W[1]-hard when parameterized either by k or by t alone, but is FPT when parameterized by k + t.

We also show that if we consider edge cuts instead of vertex cuts, the terminal variant is NP-hard.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Fedor V. Fomin
    • 1
  • Petr A. Golovach
    • 1
  • Janne H. Korhonen
    • 2
  1. 1.Department of InformaticsUniversity of BergenNorway
  2. 2.Helsinki Institute for Information Technology HIIT, & Department of Computer ScienceUniversity of HelsinkiFinland

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