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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)

Abstract

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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References

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    Brouwer, A.E., Veldman, H.J.: Contractibility and NP-completeness. Journal of Graph Theory 11, 71–79 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
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    Garey, M.R., Johnson, D.S.: Computers and Intractability. W.H. Freeman and Co., New York (1979)zbMATHGoogle Scholar
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    Robertson, N., Seymour, P.D.: Graph minors. XIII. The disjoint paths problem. Journal of Combinatorial Theory, Series B 63, 65–110 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
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    Watanabe, T., Ae, T., Nakamura, A.: On the NP-hardness of edge deletion and edge-contraction problems. Discrete Applied Mathematics 6, 63–78 (1981)CrossRefMathSciNetGoogle Scholar

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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