Skip to main content
SpringerLink
Log in

A proof of the maximal diameter conjecture for the transportation polyhedron

  • Published:
Cybernetics Aims and scope

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

Literature Cited

  1. G. B. Dantzig, Linear Programming and Extensions, Princeton Univ. Press (1963).

  2. V. Klee and D. W. Walkup, “The d-step conjecture for polyhedra of dimension d<6,” Acta Math., No. 117, 53–78 (1967).

    Google Scholar 

  3. M. L. Balinskii and A. Russakoff, “On the assignment polytope,” SIAM Rev.,16, No. 4, 516–525 (1974).

    Google Scholar 

  4. R. Saigal, “A proof of the Hirsch conjecture on the polyhedron of the shortest route problem,” SIAM J. Appl. Math.,17, No. 6, 1232–1238 (1969).

    Google Scholar 

  5. V. A. Emelichev, M. M. Kovalev, and M. K. Kravtsov, Polyhedra, Graphs, Optimization [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  6. M. L. Balinskii, “On two special classes of transportation polytopes,” Math. Program. Study, No. 1, 43–58 (1974).

    Google Scholar 

  7. A. P. Krachkovskii and V. A. Emelichev, “An upper bound on the diameter of the transportation polyhedron,” Dokl. Akad. Nauk BSSR,23, No. 4, 297–299 (1979).

    Google Scholar 

  8. V. A. Emelichev and M. K. Kravtsov, “Complexity bounds for transportation algorithms,” Kibernetika, No. 6, 124–126 (1981).

    Google Scholar 

  9. M. K. Kravtsov, “Upper bounds on the diameter of the transportation polyhedron,” in: 5th All-Union Conf. on Topics of Theoretical Cybernetics, Abstracts of Papers [in Russian], SO IM Akad. Nauk SSSR, Novosibirsk (1980), pp. 145–146.

    Google Scholar 

  10. M. K. Kravtsov, “On complexity of transportation algorithm in linear programming,” in: Mathematical Models and Optimal Planning Methods [in Russian], NIIÉMP pri Gosplane BSSR, Minsk (1980), pp. 36–50.

    Google Scholar 

  11. V. A. Emelichev, M. K. Kravtsov, and A. P. Krachkovskii, “On some classes of transportation polyhedra,” Dokl. Akad. Nauk SSSR,241, No. 3, 532–535 (1978).

    Google Scholar 

  12. V. A. Emelichev, M. K. Kravtsov, and A. P. Krachkovskii, “Transportation polyhedra with a given number of faces and a maximal number of vertices,” in: Topics in Software of Computerized Systems [in Russian], NIIÉMP pri Gosplane BSSR, Minsk (1979), pp. 26–39.

    Google Scholar 

  13. V. A. Emelichev and M. K. Kravtsov, “On some properties of transportation polyhedra with maximal number of vertices,” Dokl. Akad. Nauk SSSR,228, No. 5, 1025–1028 (1976).

    Google Scholar 

  14. M. K. Kravtsov, “The maximal diameter conjecture for transportation polyhedra,” Dokl. Akad. Nauk BSSR,27, No. 2, 132–134 (1983).

    Google Scholar 

  15. M. K. Kravtsov, “The diameter and the radius of the transportation polyhedron,” Dokl. Akad. Nauk BSSR,27, No. 2, 278–281 (1983).

    Google Scholar 

Download references

Authors
  1. M. K. Kravtsov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Kibernetika, No. 4, pp. 79–82, July–August, 1985.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kravtsov, M.K. A proof of the maximal diameter conjecture for the transportation polyhedron. Cybern Syst Anal 21, 514–519 (1985). https://doi.org/10.1007/BF01070611

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01070611

Keywords

Search

Navigation