Skip to main content
SpringerLink
Log in

Classifying the Clique-Width of H-Free Bipartite Graphs

  • Conference paper
Computing and Combinatorics (COCOON 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8591))

Included in the following conference series:

Abstract

Let G be a bipartite graph, and let H be a bipartite graph with a fixed bipartition (B H ,W H ). We consider three different, natural ways of forbidding H as an induced subgraph in G. First, G is H-free if it does not contain H as an induced subgraph. Second, G is strongly H-free if G is H-free or else has no bipartition (B G ,W G ) with B H  ⊆ B G and W H  ⊆ W G . Third, G is weakly H-free if G is H-free or else has at least one bipartition (B G ,W G ) with \(B_H\not\subseteq B_G\) or \(W_H\not\subseteq W_G\). Lozin and Volz characterized all bipartite graphs H for which the class of strongly H-free bipartite graphs has bounded clique-width. We extend their result by giving complete classifications for the other two variants of H-freeness.

The research in this paper was supported by EPSRC (EP/G043434/1 and EP/K025090/1) and ANR (TODO ANR-09-EMER-010).

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. Boliac, R., Lozin, V.: On the clique-width of graphs in hereditary classes. In: Bose, P., Morin, P. (eds.) ISAAC 2002. LNCS, vol. 2518, pp. 44–54. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  2. Bonomo, F., Grippo, L.N., Milanič, M., Safe, M.D.: Graphs of power-bounded clique-width. arXiv, abs/1402.2135 (2014)

    Google Scholar 

  3. Brandstädt, A., Engelfriet, J., Le, H.-O., Lozin, V.: Clique-width for 4-vertex forbidden subgraphs. Theory of Computing Systems 39(4), 561–590 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  4. Brandstädt, A., Klembt, T., Mahfud, S.: P 6- and triangle-free graphs revisited: structure and bounded clique-width. Discrete Mathematics and Theoretical Computer Science 8(1), 173–188 (2006)

    MathSciNet  Google Scholar 

  5. Brandstädt, A., Kratsch, D.: On the structure of (P 5,gem)-free graphs. Discrete Applied Mathematics 145(2), 155–166 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Brandstädt, A., Le, H.-O., Mosca, R.: Gem- and co-gem-free graphs have bounded clique-width. International Journal of Foundations of Computer Science 15(1), 163–185 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Brandstädt, A., Le, H.-O., Mosca, R.: Chordal co-gem-free and (P 5,gem)-free graphs have bounded clique-width. Discrete Applied Mathematics 145(2), 232–241 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  8. Brandstädt, A., Mahfud, S.: Maximum weight stable set on graphs without claw and co-claw (and similar graph classes) can be solved in linear time. Information Processing Letters 84(5), 251–259 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Brandstädt, A., Mosca, R.: On variations of P 4-sparse graphs. Discrete Applied Mathematics 129(2-3), 521–532 (2003)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  11. Dabrowski, K.K., Golovach, P.A., Paulusma, D.: Colouring of graphs with Ramsey-type forbidden subgraphs. Theoretical Computer Science 522, 34–43 (2013)

    Article  MathSciNet  Google Scholar 

  12. Dabrowski, K.K., Paulusma, D.: Clique-width of graph classes defined by two forbidden induced subgraphs. coRR, abs/1405.7092 (2014)

    Google Scholar 

  13. Gurski, F.: Graph operations on clique-width bounded graphs. CoRR, abs/cs/0701185 (2007)

    Google Scholar 

  14. Kamiński, M., Lozin, V., Milanič, M.: Recent developments on graphs of bounded clique-width. Discrete Applied Mathematics 157(12), 2747–2761 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  15. Kobler, D., Rotics, U.: Edge dominating set and colorings on graphs with fixed clique-width. Discrete Applied Mathematics 126(2-3), 197–221 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  16. Lozin, V., Rautenbach, D.: On the band-, tree-, and clique-width of graphs with bounded vertex degree. SIAM Journal on Discrete Mathematics 18(1), 195–206 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  17. Lozin, V., Rautenbach, D.: The tree- and clique-width of bipartite graphs in special classes. Australasian Journal of Combinatorics 34, 57–67 (2006)

    MATH  MathSciNet  Google Scholar 

  18. Lozin, V., Volz, J.: The clique-width of bipartite graphs in monogenic classes. International Journal of Foundations of Computer Science 19(02), 477–494 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  19. Makowsky, J., Rotics, U.: On the clique-width of graphs with few P 4’s. International Journal of Foundations of Computer Science 10(3), 329–348 (1999)

    Article  MathSciNet  Google Scholar 

  20. Oum, S.-I.: Approximating rank-width and clique-width quickly. ACM Trans. Algorithms 5(1), 10:1–10:20 (2008)

    Google Scholar 

  21. Rao, M.: MSOL partitioning problems on graphs of bounded treewidth and clique-width. Theoretical Computer Science 377(1-3), 260–267 (2007)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Engineering and Computing Sciences, Durham University, Science Laboratories, South Road, Durham, DH1 3LE, United Kingdom

    Konrad Kazimierz Dabrowski & Daniël Paulusma

Authors
  1. Konrad Kazimierz Dabrowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniël Paulusma
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1410, 30303, Atlanta, GA, USA

    Zhipeng Cai

  2. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1443, 30303, Atlanta, GA, USA

    Alex Zelikovsky

  3. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1449, 30303, Atlanta, GA, USA

    Anu Bourgeois

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Dabrowski, K.K., Paulusma, D. (2014). Classifying the Clique-Width of H-Free Bipartite Graphs. In: Cai, Z., Zelikovsky, A., Bourgeois, A. (eds) Computing and Combinatorics. COCOON 2014. Lecture Notes in Computer Science, vol 8591. Springer, Cham. https://doi.org/10.1007/978-3-319-08783-2_42

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-08783-2_42

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08782-5

  • Online ISBN: 978-3-319-08783-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation