On the planar integer two-flow problem

Abstract

We consider the two-commodity flow problem and give a good characterization of the optimum flow if the augmented network (with both source-sink edges added) is planar. We show that max flow ≧ min cut −1, and describe the structure of those networks for which equality holds.

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

References

  1. [1]

    G. M. Adelson-Velski, E. A. Dinitz andA. V. Karzanov,Algorithms for Flows in Networks (in Russian), Nauka, Moscow, 1975.

    Google Scholar 

  2. [2]

    B. V. Cherkasski, On Multiterminal Two-commodity Network Flow Problems, In:Issledovaniya po Diskretnoi Optimizacii (in Russian), Nauka, Moscow, 1976, 261–289.

    Google Scholar 

  3. [3]

    S. V. Even, A. Itai andA. Shamir, On the complexity of the timetable and multicommodity flow problem,SIAM J. Comput.,5 (4) (1976).

  4. [4]

    L. R. Ford andD. R. Fulkerson,Flows in Networks, Princeton, 1962.

  5. [5]

    T. C. Hu,Integer Programming and Network Flow, Addison—Wesley, Reading, Mass., 1970.

    Google Scholar 

  6. [6]

    A. V. Karzanov andM. V. Lomonosov, Multiflows in Undirected Networks, In:Mathematical Programming. The Problems of Social and Economic Systems, Operations Research Models 1 (in Russian) The Institute for Systems Studies, Moscow, 1978.

    Google Scholar 

  7. [7]

    P. D. Seymour, The Matroids with the Max-flow Min-cut Property.J. Comb. Theory Ser. B. 23 (1977) 189–222.

    MATH  Article  MathSciNet  Google Scholar 

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lomonosov, M.V. On the planar integer two-flow problem. Combinatorica 3, 207–218 (1983). https://doi.org/10.1007/BF02579295

Download citation

AMS subject classification (1980)

  • 90 B 10
  • 90 C 10