The Complexity of Graph Contractions

  • Asaf Levin
  • Daniël Paulusma
  • Gerhard J. Woeginger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2880)


For a fixed pattern graph H, let H-CONTRACTIBILITY denote the problem of deciding whether a given input graph is contractible to H. We continue a line of research that was started in 1987 by Brouwer & Veldman, and we determine the computational complexity of H-CONTRACTIBILITY for certain classes of pattern graphs. In particular, we pin-point the complexity for all graphs H with five vertices.

Interestingly, in all cases that are known to be polynomially solvable, the pattern graph H has a dominating vertex, whereas in all cases that are known to be NP-complete, the pattern graph H does not have a dominating vertex.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Asaf Levin
    • 1
  • Daniël Paulusma
    • 2
  • Gerhard J. Woeginger
    • 2
  1. 1.Department of Statistics and Operations ResearchTel Aviv UniversityTel AvivIsrael
  2. 2.Faculty of Mathematical SciencesUniversity of TwenteEnschedeThe Netherlands

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