Skip to main content

(K4-e)-free perfect graphs and star cutsets

Seminars

Part of the Lecture Notes in Mathematics book series (LNMCIME,volume 1403)

Abstract

We show that a perfect graph not containing (K4-e) as an induced subgraph, and whose clique-node incidence matrix does not belong to a restricted class of totally unimodular matrices, has a star cutset. This result yields a new proof that the Strong Perfect Graph Conjecture is true for this class of graphs.

Keywords

  • Incidence Matrix
  • Maximal Clique
  • Perfect Graph
  • Consecutive Node
  • Unimodular Matrice

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berge, C., "Farbung von Graphen, deren samtliche bzw deren ungerade kreise starr sind (Zusammenfassung)," Will. Z. Martin Luther Univ., Halle Wittenberg Math. Natur. Reihe, 114, 1961.

    Google Scholar 

  2. Berge, C., "Graphs and Hypergraphs," North Holland, 1973.

    Google Scholar 

  3. Berge, C., and Chvátal, V., "Topics on perfect graphs," Annals of Discrete Mathematics 21, North Holland, 1984.

    Google Scholar 

  4. Chvátal, V., Star cutsets and perfect graphs, Technical Report, SOCS, McGill University, 1983.

    Google Scholar 

  5. Conforti, M., and Cornuéjols, G., "An algorithmic framework for the matching problem in some hypergraphs," Working Paper 24-84-85, G.S.I.A., Carnegie Mellon University, To appear in Networks.

    Google Scholar 

  6. Conforti, M., Corneil, D., and Mahjoub, A. R., "Ki-covers I: Complexity and polytopes," to appear in Discrete Mathematics.

    Google Scholar 

  7. Conforti, M., Corneil, D., and Mahjoub, A. R., "Ki-covers II: Ki-perfect graphs," submitted for publication.

    Google Scholar 

  8. Lovász, L., "Normal hypergraphs and the perfect graph conjecture," Discrete Mathematics 2, 253–267, 1972.

    CrossRef  Google Scholar 

  9. Padberg, M., "Perfect zero-one matrices," Mathematical Programming 6, 180–196, 1974.

    CrossRef  Google Scholar 

  10. Parthasarathy, K. R., and Ravindra, G., "The strong perfect-graph conjecture is true for K1,3-free graphs," J. Combin. Theory B 21, 212–223, 1976.

    CrossRef  Google Scholar 

  11. Parthasarathy, K. R., and Ravindra, G., "The validity of the strong perfect-graph conjecture for (K4-e)-free graphs," J. Combin. Theory B 26, 98–100, 1979.

    CrossRef  Google Scholar 

  12. Tucker, A., "The strong perfect graph conjecture for planar graphs," Canad. J. Math. 25, 103–114, 1973a.

    CrossRef  Google Scholar 

  13. Tucker, A., Circular arc graphs: New uses and a new algorithm, in "Theory and Application of Graphs," Lecture Notes in Math 642, pp. 580–589, Springer-Verlag, 1978.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1989 Springer-Verlag

About this paper

Cite this paper

Conforti, M. (1989). (K4-e)-free perfect graphs and star cutsets. In: Simeone, B. (eds) Combinatorial Optimization. Lecture Notes in Mathematics, vol 1403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083468

Download citation

  • DOI: https://doi.org/10.1007/BFb0083468

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51797-9

  • Online ISBN: 978-3-540-46810-3

  • eBook Packages: Springer Book Archive