Skip to main content

The pathwidth and treewidth of cographs

  • Conference paper
  • First Online:
SWAT 90 (SWAT 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 447))

Included in the following conference series:

Abstract

It is shown that the pathwidth of a cograph equals its treewidth, and a linear time algorithm to determine the pathwidth of a the cograph and build a corresponding path-decomposition is given.

The research of this author was partially supported by the ESPRIT II Basic Research Actions Program of the EC under Contract No. 3075 (project ALCOM).

The research of this author was partially supported by the Deutsche Forschungsgemeinschaft under Grant No. Mo446/1-1.

The research of this author was partially supported by the ESPRIT II Basic Research Actions Program of the EC under Contract No. 3075 (project AlCOM).

The research of this author was partially supported by the Deutsche Forschungsgemeinschaft under Grant No. Mo446/1-1.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Arnborg. Efficient algorithms for combinatorial problems on graphs with bounded decomposability — A Survey. BIT, 25:2–23, 1985.

    Google Scholar 

  2. S. Arnborg, D.G. Corneil and A. Proskurowski. Complexity of finding embeddings in a κ-tree. SIAM J. Alg. Disc. Meth., 8:277–284, 1987.

    Google Scholar 

  3. H.L. Bodlaender. Classes of graphs with bounded treewidth. Technical Report RUU-CS-86-22, Dept. of Computer Science, University of Utrecht, Utrecht, 1986.

    Google Scholar 

  4. H.L. Bodlaender. Dynamic programming algorithms on graphs with bounded tree-width. Techn. rep., Lab. for Computer Science, M.I.T., 1987. Ext. abstract in proceedings ICALP 88.

    Google Scholar 

  5. H.L. Bodlaender. Improved self-reduction algorithms for graphs with bounded treewidth. Technical Report RUU-CS-88-29, Dept. of Computer Science, Univ. of Utrecht, 1988. To appear in: Proc. Workshop on Graph Theoretic Concepts in Comp. Sc. '89.

    Google Scholar 

  6. D.G. Corneil, H. Lerchs, and L. Stewart Burlingham. Complement reducible graphs, Disc. Appl. Math. 3: 163–174, 1981.

    Article  Google Scholar 

  7. D.G Corneil, Y. Perl and L. Stewart. A linear recognition for cographs. SIAM J. Comput., 4:926–934, 1985.

    Google Scholar 

  8. J. Ellis, I.H. Sudborough, and J. Turner. Graph separation and search number. Report DCS-66-IR, University of Victoria, 1987.

    Google Scholar 

  9. M.C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York, 1980.

    Google Scholar 

  10. J. Gustedt. Path width for chordal graphs is NP-complete. Preprint TU Berlin, 1989.

    Google Scholar 

  11. L.M. Kirousis and C.H. Papadimitriou. Interval graphs and searching. Disc. Math., 55:181–184, 1985.

    Google Scholar 

  12. L.M. Kirousis and C.H. Papadimitriou. Searching and pebbling. Theor. Comp. Sc., 47:205–218, 1986.

    Article  Google Scholar 

  13. R.H. Möhring. Graph problems related to gate matrix layout and PLA folding. Technical Report 223/1989, Department of Mathematics, Technical University of Berlin, 1989.

    Google Scholar 

  14. M.B. Novick. Fast parallel algorithms for the modular decomposition. Technical Report TR 89-1016, Department of Computer Science, Cornell University, 1989.

    Google Scholar 

  15. N. Robertson and P. Seymour. Graph minors. I. Excluding a forest. J. Comb. Theory Series B, 35:39–61, 1983.

    Google Scholar 

  16. N. Robertson and P. Seymour. Graph minors. II. Algorithmic aspects of tree-width. J. Algorithms, 7:309–322, 1986.

    Article  Google Scholar 

  17. N. Robertson and P. Seymour. Graph minors. XIII. The disjoint paths problem. Manuscript, 1986.

    Google Scholar 

  18. P. Scheffler. Die Baumweite von Graphen als ein Maß für die Kompliziertheit algorithmischer Probleme. PhD thesis, Akademie der Wissenschaften der DDR, Berlin, 1989.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

John R. Gilbert Rolf Karlsson

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bodlaender, H.L., Möhring, R.H. (1990). The pathwidth and treewidth of cographs. In: Gilbert, J.R., Karlsson, R. (eds) SWAT 90. SWAT 1990. Lecture Notes in Computer Science, vol 447. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52846-6_99

Download citation

  • DOI: https://doi.org/10.1007/3-540-52846-6_99

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52846-3

  • Online ISBN: 978-3-540-47164-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics