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The Complexity of Graph Contractions

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Graph-Theoretic Concepts in Computer Science (WG 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2880))

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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

  1. Brouwer, A.E., Veldman, H.J.: Contractibility and NP-completeness. Journal of Graph Theory 11, 71–79 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  2. Garey, M.R., Johnson, D.S.: Computers and Intractability. W.H. Freeman and Co., New York (1979)

    MATH  Google Scholar 

  3. Robertson, N., Seymour, P.D.: Graph minors. XIII. The disjoint paths problem. Journal of Combinatorial Theory, Series B 63, 65–110 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  4. Watanabe, T., Ae, T., Nakamura, A.: On the NP-hardness of edge deletion and edge-contraction problems. Discrete Applied Mathematics 6, 63–78 (1981)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Statistics and Operations Research, Tel Aviv University, Tel Aviv, 69978, Israel

    Asaf Levin

  2. Faculty of Mathematical Sciences, University of Twente, 7500 AE, Enschede, The Netherlands

    Daniël Paulusma & Gerhard J. Woeginger

Authors
  1. Asaf Levin
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  2. Daniël Paulusma
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  3. Gerhard J. Woeginger
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Editor information

Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, The Netherlands

    Hans L. Bodlaender

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© 2003 Springer-Verlag Berlin Heidelberg

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Levin, A., Paulusma, D., Woeginger, G.J. (2003). The Complexity of Graph Contractions. In: Bodlaender, H.L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2003. Lecture Notes in Computer Science, vol 2880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39890-5_28

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  • DOI: https://doi.org/10.1007/978-3-540-39890-5_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20452-7

  • Online ISBN: 978-3-540-39890-5

  • eBook Packages: Springer Book Archive

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