Skip to main content
Log in

Classification of polyhedral matroids

  • Published:
Mathematical Methods of Operations Research Aims and scope Submit manuscript

Abstract

This paper establishes polyhedral properties of matroidal structures. Classical problems such as enumeration and classification of polyhedra matroids, the characterization of face complexes, the metric properties of graphs of polymatroids are considered.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Aleksandrov A (1958) Konvexe Polyeder. Berlin

  2. Bixby RE, Cunningham WH, Topkis DM (1985) The partial order of a polymatroid extreme point. Mathematics of Operations Research 10:367–378

    Article  MATH  MathSciNet  Google Scholar 

  3. Broensted A (1983) An introduction to convex polytopes. Springer, New York, Heidelberg, Berlin 240

    Google Scholar 

  4. Dimov E, Kovalev M (1983) Symmetrical polymatroids. Proceedings of the international conference. Mathematical methods in optimization. Sofia 24–25

  5. Edmonds J, Guy, Hanani, Sauer, Schönheim (ed) (1970) Submodular functions, matroids and certain polyhedra. Proceedings of the Calgary International Conference on Combinatorial Structures and their Applications. Gordon and Breach, New York 69–87

  6. Edmonds J, Giles R (1977) A min-max relation for submodular functions on graphs. Annals of Discrete Mathematics 1:185–204

    Article  MATH  MathSciNet  Google Scholar 

  7. Faigle U (1987) Matroids in combinatorial optimization. In: Combinatorial geometries, Encyclopedia of mathematics and its application. Cambridge University Press

  8. Federico P (1982) Descartes on Polyhedra

  9. Frank A (1984) Generalized polymatroids. Proceedings of the 6. Hungarian Combinatorial Colloquium. Eger

  10. Fujishige S (1984) A note on Frank's generalized polymatroids. Discrete Applied Mathematics 7:105–109

    Article  MATH  MathSciNet  Google Scholar 

  11. Girlich E, Kovalev MM (1980) Zur mathematischen Theorie der optimalen Standardisierung. MOS, series optimization 11:547–561

    MATH  Google Scholar 

  12. Girlich E, Kovalev MM (1985) Klassifizierung von Polymatroiden. In: Diskrete Optimierung, Wiss Beitraege der FSU Jena 6–21

  13. Kovalev MM (1985) The cone of the symmetric submodular functions. Cybernetics 5

  14. Kovalev MM, Isachenko A (1978) Linearization of combinatorial optimization problems (russ) Dokl AN BSSR 869–872

  15. Kovalev MM, Pisaruk NN (1984) Generalized matroids (russ) Dokl AN BSSR 11:972–995

    MathSciNet  Google Scholar 

  16. McMullen P, Shepard G (1971) Convex polytopes and the upper bound conjecture. Cambridge University Press

  17. Yemelichev VA, Kovalev MM, Kravtsov MK (1984) Polytopes, graphs and optimization. Cambridge University Press

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported by DAAD and Belarussian Fundamental Science Fund

Rights and permissions

Reprints and permissions

About this article

Cite this article

Girlich, E., Kovalev, M. Classification of polyhedral matroids. Mathematical Methods of Operations Research 43, 143–159 (1996). https://doi.org/10.1007/BF01680368

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01680368

Key words

Navigation