Parameterized complexity of critical node cuts

Danny Hermelin, Moshe Kaspi, Christian Komusiewicz, Barak Navon

Research output: Contribution to journalArticlepeer-review


We consider the following graph cut problem called CRITICAL NODE CUT (CNC): Given a graph G on n vertices, and two positive integers k and x, determine whether G has a set of k vertices whose removal leaves G with at most x connected pairs of vertices. We analyze this problem in the framework of parameterized complexity. That is, we are interested in whether or not this problem is solvable in f(κ)⋅nO(1) time (i.e., whether or not it is fixed-parameter tractable), for various natural parameters κ. We consider four such parameters: • The size k of the required cut.• The upper bound x on the number of remaining connected pairs.• The lower bound y on the number of connected pairs to be removed.• The treewidth w of G.We determine whether or not CNC is fixed-parameter tractable for each of these parameters. We determine this also for all possible aggregations of these four parameters, apart from w+k. Moreover, we also determine whether or not CNC admits a polynomial kernel for all these parameterizations. That is, whether or not there is an algorithm that reduces each instance of CNC in polynomial time to an equivalent instance of size κO(1), where κ is the given parameter.

Original languageAmerican English
Pages (from-to)62-75
Number of pages14
JournalTheoretical Computer Science
StatePublished - 25 Oct 2016


  • Graph cut problems
  • Kernelization
  • Treewidth

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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