Skip to main content
SpringerLink
Log in

Complexity Issues in Switching of Graphs

  • Conference paper
Theory and Application of Graph Transformations (TAGT 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1764))

Abstract

In the context of graph transformations we look at the operation of switching, which can be viewed as an elegant method for realizing global transformations of graphs through local transformations of the vertices. We compare the complexity of a number of problems on graphs with the complexity of these problems extended to the set of switches of a graph. Within this framework, we prove a modification of Yannakakis’ result and use it to show NP-completeness for the embedding problem. Finally we prove NP-completeness for the 3-colourability problem.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Corneil, D.G., Mathon, R.A. (eds.): Geometry and Combinatorics: Selected Works of J. J. Seidel. Academic Press, London (1991)

    Google Scholar 

  2. Ehrenfeucht, A., Hage, J., Harju, T., Rozenberg, G.: Pancyclicity in switching classes (submitted)

    Google Scholar 

  3. Ehrenfeucht, A., Rozenberg, G.: An introduction to dynamic labeled 2-structures. In: Borzyszkowski, A.M., Sokolowski, S. (eds.) MFCS 1993. LNCS, vol. 711, pp. 156–173. Springer, Berlin (1993)

    Google Scholar 

  4. Ehrenfeucht, A., Rozenberg, G.: Dynamic labeled 2-structures. Mathematical Structures in Computer Science 4, 433–455 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  5. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)

    MATH  Google Scholar 

  6. Gross, J.L., Tucker, T.W.: Topological Graph Theory. Wiley, New York (1987)

    MATH  Google Scholar 

  7. Hage, J.: The membership problem for switching classes with skew gains. Accepted for Fundamenta Informaticae

    Google Scholar 

  8. Kratochvíl, J., Nešetřil, J., Zýka, O.: On the computational complexity of Seidel’s switching. In: Combinatorics Graphs Complexity, Prague, pp. 161–166. Prachatice (1990)

    Google Scholar 

  9. Seidel, J.J.: A survey of two-graphs. In: Colloquio Internazionale sulle Teorie Combinatorie (Rome,1973), vol. I, Rome, pp. 481–511 (1996); Acc. Naz. Lincei. Reprinted in [1]

    Google Scholar 

  10. Seidel, J.J., Taylor, D.E.: Two-graphs, a second survey. In: Lovasz, L., Sós, V.T. (eds.) Algebraic Methods in Graph Theory (Proc. Internat. Colloq., Szeged, 1978), vol. II, pp. 689–711. North-Holland, Amsterdam (1981)

    Google Scholar 

  11. Yannakakis, M.: Node- and edge-deletion NP-complete problems. In: Proc. 10th Ann. ACM Symp. on theory of Computing, pp. 253–264. ACM, New York (1978)

    Chapter  Google Scholar 

  12. Zaslavsky, T.: Biased graphs. I. Bias, balance, and gains. J. Combin. Theory, Ser. B 47, 32–52 (1989)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Leiden Institute of Advanced Computer Science, P.O. Box 9512, 2300 RA, Leiden, The Netherlands

    Jurriaan Hage & Grzegorz Rozenberg

  2. Dept. of Computer Science, University of Colorado at Boulder, Boulder, Co, 80309, U.S.A.

    Andrzej Ehrenfeucht & Grzegorz Rozenberg

  3. Dept. of Mathematics, University of Turku, FIN-20014, Turku, Finland

    Tero Harju

Authors
  1. Andrzej Ehrenfeucht
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jurriaan Hage
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tero Harju
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Grzegorz Rozenberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Technische Universität Berlin, Germany

    Hartmut Ehrig

  2. University of Paderborn, Warburger StraĂźe 100, 33098, Paderborn, Germany

    Gregor Engels

  3. Department of Computer Science, University of Bremen, P.O. Box 33 04 40, 28334, Bremen, Germany

    Hans-Jörg Kreowski

  4. Leiden Center of Advanced Computer Science (LIACS), Leiden University, Niels Bohrweg 1, 2333, Leiden, CA, The Netherlands

    Grzegorz Rozenberg

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ehrenfeucht, A., Hage, J., Harju, T., Rozenberg, G. (2000). Complexity Issues in Switching of Graphs. In: Ehrig, H., Engels, G., Kreowski, HJ., Rozenberg, G. (eds) Theory and Application of Graph Transformations. TAGT 1998. Lecture Notes in Computer Science, vol 1764. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46464-8_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-46464-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67203-6

  • Online ISBN: 978-3-540-46464-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation