Skip to main content
SpringerLink
Log in

Embedding in Switching Classes with Skew Gains

  • Conference paper
Graph Transformations (ICGT 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3256))

Included in the following conference series:

Abstract

In the context of graph transformation we look at the operation of switching, which can be viewed as an elegant method for realizing global transformations of (group-labelled) graphs through local transformations of the vertices.

Various relatively efficient algorithms exist for deciding whether a graph can be switched so that it contains some other graph, the query graph, as an induced subgraph in case vertices are given an identity. However, when considering graphs up to isomorphism, we immediately run into the graph isomorphism problem for which no efficient solution is known.

Surprisingly enough however, in some cases the decision process can be simplified by transforming the query graph into a “smaller” graph without changing the answer. The main lesson learned is that the size of the query graph is not the dominating factor, but its cycle rank.

Although a number of our results hold specifically for undirected, unlabelled graphs, we propose a more general framework and give some preliminary results for more general cases, where the graphs are labelled with elements of a group.

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. Ehrenfeucht, A., Hage, J., Harju, T., Rozenberg, G.: Complexity issues in switching of graphs. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) TAGT 1998. LNCS, vol. 1764, pp. 59–70. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  2. Ehrenfeucht, A., Harju, T., Rozenberg, G.: The Theory of 2-Structures. World Scientific, Singapore (1999)

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  5. Hage, J.: The membership problem for switching classes with skew gains. Fundamenta Informaticae 39(4), 375–387 (1999)

    MATH  MathSciNet  Google Scholar 

  6. Hage, J., Harju, T., Welzl, E.: Euler graphs, triangle-free graphs and bipartite graphs in swithing classes. Fundamenta Informaticae 58(1), 23–37 (2003)

    MATH  MathSciNet  Google Scholar 

  7. Rotman, J.J.: The Theory of Groups, 2nd edn. Allyn and Bacon, Boston (1973)

    MATH  Google Scholar 

  8. Zaslavsky, T.: Signed graphs. Discrete Applied Math. 4, 47–74 (1982); Erratum on p. 248 of volume 5.

    Article  MATH  MathSciNet  Google Scholar 

  9. 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. Inst. of Information and Computing Sci, Univ. Utrecht, P.O.Box 80.089, 3508 TB, Utrecht, The Netherlands

    Jurriaan Hage

  2. Dept. of Computer Science, University of Colorado at Boulder, Boulder, CO, 80309, USA

    Andrzej Ehrenfeucht & Grzegorz Rozenberg

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

    Tero Harju

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

    Grzegorz Rozenberg

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 Straße 100, 33098, Paderborn, Germany

    Gregor Engels

  3. George Mason University, Fairfax, Virginia, USA

    Francesco Parisi-Presicce

  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

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ehrenfeucht, A., Hage, J., Harju, T., Rozenberg, G. (2004). Embedding in Switching Classes with Skew Gains. In: Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds) Graph Transformations. ICGT 2004. Lecture Notes in Computer Science, vol 3256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30203-2_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30203-2_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23207-0

  • Online ISBN: 978-3-540-30203-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation