On Contracting Graphs to Fixed Pattern Graphs

  • Pim van ’t Hof
  • Marcin Kamiński
  • Daniël Paulusma
  • Stefan Szeider
  • Dimitrios M. Thilikos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5901)


For a fixed graph H, the H-Contractibility problem asks if a graph is H-contractible, i.e., can be transformed into H via a series of edge contractions. The computational complexity classification of this problem is still open. So far, H has a dominating vertex in all cases known to be polynomially solvable, whereas H does not have such a vertex in all cases known to be NP-complete. Here, we present a class of graphs H with a dominating vertex for which H-Contractibility is NP-complete. We also present a new class of graphs H for which H-Contractibility is polynomially solvable. Furthermore, we study the (H,v)-Contractibility problem, where v is a vertex of H. The input of this problem is a graph G and an integer k. The question is whether G is H-contractible such that the “bag” of G corresponding to v contains at least k vertices. We show that this problem is NP-complete whenever H is connected and v is not a dominating vertex of H.


Polynomial Time Connected Graph Pendant Vertex Edge Contraction Vertex Deletion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Pim van ’t Hof
    • 1
  • Marcin Kamiński
    • 2
  • Daniël Paulusma
    • 1
  • Stefan Szeider
    • 1
  • Dimitrios M. Thilikos
    • 3
  1. 1.School of Engineering and Computing SciencesUniversity of Durham, Science LaboratoriesDurhamEngland
  2. 2.Computer Science DepartmentUniversité Libre de BruxellesBrusselsBelgium
  3. 3.Department of MathematicsNational and Kapodistrian University of AthensAthensGreece

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