Edge-Editing to a Dense and a Sparse Graph Class

  • Michal Kotrbčík
  • Rastislav Královič
  • Sebastian OrdyniakEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9644)


We consider a graph edge-editing problem, where the goal is to transform a given graph G into a disjoint union of two graphs from a pair of given graph classes, investigating what properties of the classes make the problem fixed-parameter tractable. We focus on the case when the first class is dense, i.e. every such graph G has minimum degree at least \(|V(G)| - \delta \) for a constant \(\delta \), and assume that the cost of editing to this class is fixed-parameter tractable parameterized by the cost. Under the assumptions that the second class either has bounded maximum degree, or is edge-monotone, can be defined in \(\text {MSO}_2\), and has bounded treewidth, we prove that the problem is fixed-parameter tractable parameterized by the cost. We also show that the problem is fixed-parameter tractable parameterized by degeneracy if the second class consists of independent sets and Subgraph Isomorphism is fixed-parameter tractable for the input graphs. On the other hand, we prove that parameterization by degeneracy is in general \(\text { W[1]}\)-hard even for editing to cliques and independent sets.


Graph modification problems Clique-editing Degeneracy Parameterized complexity Treewidth 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Michal Kotrbčík
    • 1
  • Rastislav Královič
    • 2
  • Sebastian Ordyniak
    • 3
    Email author
  1. 1.Faculty of InformaticsMasaryk UniversityBrnoCzech Republic
  2. 2.Department of Computer ScienceComenius UniversityBratislavaSlovakia
  3. 3.Institute of Information SystemsTU WienViennaAustria

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