Skip to main content
SpringerLink
Log in

The Tree-Width of Clique-Width Bounded Graphs without Kn,n

  • Conference paper
  • First Online:
Graph-Theoretic Concepts in Computer Science (WG 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1928))

Included in the following conference series:

Abstract

We proof that every graph of clique-width k which does not contain the complete bipartite graph Kn,n for some n > 1 as a subgraph has tree-width at most 3k(n - 1) - 1. This immediately implies that a set of graphs of bounded clique-width has bounded tree-width if it is uniformly l-sparse, closed under subgraphs, of bounded degree, or planar.

The work of the first author was supported by the German Research Association (DFG) grant WA 674/9-1.

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. S. Arnborg, J. Lagergren, and D. Seese. Easy problems for tree-decomposable graphs. Journal of Algorithms, 12308–340, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  2. H.L. Bodlaender. A partial k-arboretum of graphs with bounded treewidth. Theoretical Computer Science, 209:1–45, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  3. B.D.G. Corneil, M. Habib, J.M. Lanlignel, B. Reed, and U. Rotics. Polynomial time recognition of clique-width at most three graphs. In Proceedings of Latin American Symposium on Theoretical Informatics (LATIN’ 2000), volume 1776 of LNCS. Springer-Verlag, 2000.

    Google Scholar 

  4. B. Courcelle, J.A. Makowsky, and U. Rotics. Linear time solvable optimization problems on graphs of bounded clique width, extended abstract. In Proceedings of Graph-Theoretical Concepts in Computer Science, volume 1517 of LNCS, pages 1–16. Springer-Verlag, 1998.

    Google Scholar 

  5. B. Courcelle and S. Olariu. Upper bounds to the clique width of graphs. Discrete Applied Mathematics, 101:77–114, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  6. B. Courcelle. The monadic second-order logic of graphs I: Recognizable sets of finite graphs. Information and Computation, 85:12–75, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  7. B. Courcelle. The monadic second-order logic of graphs XIV: Uniformly sparse graphs and edge set quantifications. submitted for publication, 2000.

    Google Scholar 

  8. D.G. Corneil, Y. Perl, and L.K. Stewart. A linear recognition algorithm for cographs. SIAM Journal on Computing, 14(4):926–934, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  9. M.C. Golumbic and U. Rotics. On the clique-width of perfect graph classes. In Proceedings of Graph-Theoretical Concepts in Computer Science, volume 1665 of LNCS, pages 135–147. Springer-Verlag, 1999.

    Google Scholar 

  10. F. Gurski. Algorithmische Charakterisierungen spezieller Graphklassen. Diplomarbeit, Heinrich-Heine-Universität, Düsseldorf, Germany, 1998.

    Google Scholar 

  11. Ö. Johansson. Clique-decomposition, NLC-decomposition, and modular decomposition-relationships and results for random graphs. Congressus Numerantium, 132:39–60, 1998.

    Google Scholar 

  12. Ö. Johansson. NLC2 decomposition in polynomial time. In Proceedings of GraphTheoretical Concepts in Computer Science, volume 1665 of LNCS, pages 110–121.Springer-Verlag, 1999.

    Google Scholar 

  13. N. Robertson and P.D. Seymour. Graph minors II. Algorithmic aspects of tree width. Journal of Algorithms, 7:309–322, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  14. E. Wanke. k-NLC graphs and polynomial algorithms. Discrete Applied Mathematics, 54:251–266, 1994.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Mathematical Institute, Heinrich-Heine-University, 40225, Düsseldorf, Germany

    Frank Gurski & Egon Wanke

Authors
  1. Frank Gurski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Egon Wanke
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer and Information Science, University of Konstanz, Box D 188, 78457, Konstanz, Germany

    Ulrik Brandes  & Dorothea Wagner  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gurski, F., Wanke, E. (2000). The Tree-Width of Clique-Width Bounded Graphs without Kn,n . In: Brandes, U., Wagner, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2000. Lecture Notes in Computer Science, vol 1928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40064-8_19

Download citation

  • DOI: https://doi.org/10.1007/3-540-40064-8_19

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41183-3

  • Online ISBN: 978-3-540-40064-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation