Skip to main content
SpringerLink
Log in

On the Clique-Width of Graphs in Hereditary Classes

  • Conference paper
  • First Online:
Algorithms and Computation (ISAAC 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2518))

Included in the following conference series:

Abstract

The paper presents several results that can be helpful for deciding whether the clique-width of graphs in a certain class is bounded or not, and applies these results to a number of particular graph classes.

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. Alekseev V.: On lower layers of the lattice of hereditary classes of graphs. Diskretn. Anal. Issled. Oper. Ser. 14(1) (1997) 3–12 (in Russian)

    Google Scholar 

  2. Boliac R., Lozin V.V.: An attractive class of bipartite graphs. Discuss. Math. Graph Theory 21(2) (2001) 293–301

    MATH  MathSciNet  Google Scholar 

  3. Bollobas B.: Extremal graph theory. Acad. Press, London (1978)

    MATH  Google Scholar 

  4. Brandstädt A., Lozin V.V.: On the linear structure and clique-width of bipartite permutation graphs. Ars Combinatoria, to appear

    Google Scholar 

  5. Chen H.-C., Wang Y.-L.: An efficient algorithm for generating Prüfer codes from labeled trees. Theory Comput. Systems 33 (2000) 97–105

    Article  MATH  Google Scholar 

  6. Courcelle B.: Graph grammars, monadic second-order logic and the theory of graph minors. Contemporary Mathematics 147 (1993) 565–590

    MathSciNet  Google Scholar 

  7. Courcelle B., Engelfriet J., Rozenberg G.: Handle-rewriting hypergraphs grammars. J. Comput. System Sci. 46(2) (1993) 218–270

    Article  MATH  MathSciNet  Google Scholar 

  8. Courcelle B., Makowsky J.A., Rotics U.: Linear time solvable optimization problems on graphs of bounded clique-width. Theory Comput. Syst. 33(2) (2000) 125–150

    Article  MATH  MathSciNet  Google Scholar 

  9. Courcelle B., Olariu S.: Upper bounds to the clique-width of a graph. Discrete Appl. Math. 101(1–3) (2000) 77–114

    Article  MATH  MathSciNet  Google Scholar 

  10. Erdös P., Spencer J.: Probabilistic methods in combinatorics. Probability and Mathematical Statistics, Vol. 17. Academic Press, New York-London (1974)

    Google Scholar 

  11. Foldes S., Hammer P.L.: Split graphs. Congres. Numer. 19 (1977) 311–315

    MathSciNet  Google Scholar 

  12. Fouquet J.-L., Giakoumakis V., Vanherpe J.-M.: Bipartite graphs totally decomposable by canonical decomposition. Internat. J. Found. Comput. Sci. 10(4) (1999) 513–533

    Article  MathSciNet  Google Scholar 

  13. Giakoumakis V., Vanherpe J.-M.: Bi-complement reducible graphs. Adv. in Appl. Math. 18(4) (1997) 389–402

    Article  MATH  MathSciNet  Google Scholar 

  14. Golumbic M.C., Rotics U.: On the clique-width of some perfect graph classes. Internat. J. Found. Comput. Sci. 11(3) (2000) 423–443

    Article  MathSciNet  Google Scholar 

  15. Lazebnik F., Ustimenko V.A., Woldar A.J.: A new series of dense graphs of high girth. Bull. Amer. Math. Soc. (N.S.) 32(1) (1995) 73–79

    Article  MATH  MathSciNet  Google Scholar 

  16. Lozin V.V.: E-free bipartite graphs. Diskretn. Anal. Issled. Oper. Ser. 1, 7(1) (2000) 49–66 (in Russian)

    MATH  MathSciNet  Google Scholar 

  17. Lozin V.V.: On a generalization of bi-complement reducible graphs. Lecture Notes in Comput. Sci. 1893 (2000) 528–538

    Article  MathSciNet  Google Scholar 

  18. Lozin V.V.: Bipartite graphs without a skew star. Discrete Math. 256 (2002), to appear

    Google Scholar 

  19. Makowsky J.A., Rotics U.: On the clique-width of graphs with few P4’s. Internat. J. Found. Comput. Sci. 10(3) (1999) 329–348

    Article  MathSciNet  Google Scholar 

  20. Olariu S.: Paw-free graphs. Inform. Process. Lett. 28(1) (1988) 53–54

    Article  MATH  MathSciNet  Google Scholar 

  21. Prüfer H.: Neuer Beweis eines satzes über Permutationen. Archiv der Mathematik und Physik 27 (1918) 742–744

    Google Scholar 

  22. Scheinerman E.R., Zito J.: On the size of hereditary classes of graphs. J. Combin. Theory, Ser. B 61(1) (1994) 16–39

    Article  MathSciNet  Google Scholar 

  23. Spinrad J. P.: Nonredundant 1’s in Γ-free matrices. SIAM J. Discrete Math. 8(2) (1995) 251–257

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. RUTCOR, Rutgers University, 640 Bartholomew Rd, Piscataway, NJ, 08854-8003, USA

    Rodica Boliac & Vadim Lozin

Authors
  1. Rodica Boliac
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vadim Lozin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada, K1S 5B6

    Prosenjit Bose  & Pat Morin  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Boliac, R., Lozin, V. (2002). On the Clique-Width of Graphs in Hereditary Classes. In: Bose, P., Morin, P. (eds) Algorithms and Computation. ISAAC 2002. Lecture Notes in Computer Science, vol 2518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36136-7_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-36136-7_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00142-3

  • Online ISBN: 978-3-540-36136-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation