Skip to main content
Springer Nature Link
Log in

Lift-and-project cuts and perfect graphs

  • Published:
Mathematical Programming Submit manuscript

Abstract.

We analyze the application of lift-and-project to the clique relaxation of the stable set polytope. We characterize all the inequalities that can be generated through the application of the lift-and-project procedure, introduce the concept of 1-perfection and prove its equivalence to minimal imperfection. This characterization of inequalities and minimal imperfection leads to a generalization of the Perfect Graph Theorem of Lovász, as proved by Aguilera, Escalante and Nasini [1].

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Aguilera, N., Escalante, M., Nasini, G.: A generalization of the Perfect Graph Theorem under the Disjunctive Index. Mathematics of Operations Research. To appear.

  2. Balas, E.: Disjunctive programming. Annals of Discrete Mathematics. 5, 3–51 (1979)

  3. Balas, E., Ceria, S., Cornuéjols, G.: A lift-and-project cutting plane algorithm for mixed 0–1 programs. Mathematical Programming 58, 295–324 (1993)

    Google Scholar 

  4. Berge C.: Färbung von Graphen deren sämtliche bzw. deren ungerade Kreise starr sind (Zusammenfassung), Wissenschaftliche Zeistschirft, Martin Luhter Universität Halle-Wittenberg, Mathematisch-Naturwissenchaftliche Reihe 1961, pp. 114–115

  5. Bondy, J., Murty, U.: Graph Theory with Applications. North Holland, 1976

  6. Ceria, S.: Lift-and-Project Methods for Mixed 0–1 Programs. Ph.D. Dissertation, Carnegie Mellon University, 1993

  7. Chvátal, V.: On certain polytopes associated with graphs, Journal of Combinatorial Theory (B) 18, 138–154 (1975)

    Google Scholar 

  8. Gerards, A., Maróti, G., Schrijver, A.: Note on: N. Aguilera, M. Escalante, G. Nasini, A generalization of the Perfect Graph Theorem under the Disjunctive Index, Personal Communication, 2002

  9. Lovász, L., Schrijver, A.: Cones of Matrices and Set Functions, SIAM Journal of Optimization 1, 166–190 (1991)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Axioma, Inc., New York, New York, NY, 10001

    Sebastián Ceria

Authors
  1. Sebastián Ceria
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Sebastián Ceria.

Additional information

Mathematics Subject Classification: 05C17, 90C57

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ceria, S. Lift-and-project cuts and perfect graphs. Math. Program., Ser. B 98, 309–317 (2003). https://doi.org/10.1007/s10107-003-0406-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10107-003-0406-6

Keywords