Skip to main content
SpringerLink
Log in

A note on strong perfectness of graphs

  • Published:
Mathematical Programming Submit manuscript

Abstract

In (strongly) perfect graphs, we define (strongly) canonical colorings; we show that for some classes of graphs, such colorings can be obtained by sequential coloring techniques.

Chromatic properties ofP 4-free graphs based on such coloring techniques are mentioned and extensions to graphs containing no inducedP 5,\(\bar P_5 \) orC 5 are presented. In particular we characterize the class of graphs in which any maximal (or minimal) nodex in the vicinal preorder has the following property: there is either noP 4 havingx as a midpoint or noP 4 havingx as an endpoint. For such graphs, according to a result of Chvatal, there is a simple sequential coloring algorithm.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C. Berge,Graphs and hypergraphs (North-Holland, Amsterdam, 1973).

    MATH  Google Scholar 

  2. C. Berge and P. Duchet, “Strongly perfect graphs”, to appear.

  3. C.A. Christen and S.M. Selkow, “Some perfect coloring properties of graphs”,Journal of Combinatorial Theory (B) 27 (1979) 49–59.

    Article  MATH  MathSciNet  Google Scholar 

  4. D.G. Corneil, H. Lerchs and L. Stewart Burlingham, “Complement reducible graphs”,Discrete Applied Mathematics 3 (1981) 163–174.

    Article  MATH  MathSciNet  Google Scholar 

  5. V. Chvátal, private communication.

  6. V. Chvátal, “Perfectly ordered graphs”, Technical Report SOCS-81.28 School of Computer Science, McGill University, (Montreal, 1981).

    Google Scholar 

  7. S. Foldes and P.L. Hammer, “Split graphs having Dilworth number two”,Canadian Journal of Mathematics 29 (1977) 666–672.

    MATH  MathSciNet  Google Scholar 

  8. N.V.R. Mahadev, M. Preissmann and D. de Werra, “Superbrittle and superfragile graphs,” OR-WP 84/2, Ecole Polytechnique Fédérale de Lausanne, 1984.

  9. N.V.R. Mahadev and D. de Werra, “On a class of perfectly orderable graphs”, CORR 83-27, University of Waterloo (1983).

  10. B. Roy, “Nombre chromatique et plus longs chemins d’un graphe”,R.I.R.O. 5 (1967) 129–132.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de Mathématiques Ecole Polytechnique Fédérale de Lausanne, Switzerland

    M. Preissmann & D. de Werra

Authors
  1. M. Preissmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. de Werra
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Preissmann, M., de Werra, D. A note on strong perfectness of graphs. Mathematical Programming 31, 321–326 (1985). https://doi.org/10.1007/BF02591953

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02591953

Key words

Search

Navigation