Packing directed circuits exactly

Abstract

We give an “excluded minor” and a “structural” characterization of digraphs D that have the property that for every subdigraph H of D, the maximum number of disjoint circuits in H is equal to the minimum cardinality of a set TV(H) such that H\T is acyclic.

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

References

  1. [1]

    W. McCuaig: Pólya’s permanent problem, Electron. J. Combin. 11 (2004), 83.

    MathSciNet  Google Scholar 

  2. [2]

    G. Ding and W. Zang: Packing cycles in graphs, J. Combin. Theory Ser. B 86 (2002), 381–407.

  3. [3]

    C. H. C. Little: A characterization of convertible (0, 1)-matrices, J. Combin. Theory Ser. B 18 (1975), 187–208.

    MathSciNet  MATH  Article  Google Scholar 

  4. [4]

    C. L. Lucchesi and D. H. Younger: A minimax relation for directed graphs, J. London Math. Soc. 17 (1978), 369–374.

    MathSciNet  MATH  Article  Google Scholar 

  5. [5]

    B. Reed, N. Robertson, P. D. Seymour and R. Thomas: Packing directed circuits, Combinatorica 16 (1996), 535–554.

    MathSciNet  MATH  Article  Google Scholar 

  6. [6]

    N. Robertson, P. D. Seymour and R. Thomas: Permanents, Pfaffian orientations, and even directed circuits, Ann. Math. 150 (1999), 929–975.

    MathSciNet  MATH  Article  Google Scholar 

  7. [7]

    P. D. Seymour and C. Thomassen: Characterization of even directed graphs, J. Combin. Theory Ser. B 42 (1987), 36–45.

    MathSciNet  MATH  Article  Google Scholar 

  8. [8]

    W. Zang, M. Cai and X. Deng: A TDI system and its application to approximation algorithm, Proc. 39th IEEE Symposium on Foundations of Computer Science, (1998).

  9. [9]

    W. Zang, M. Cai and X. Deng: A min-max theorem on feedback vertex sets, Math. of Operations research, 27, (2002), 361–371.

    MathSciNet  MATH  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Bertrand Guenin.

Additional information

Research partially supported by NSF under Grant No. DMS 96-32032 and Grant No. DMS-9970514.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Guenin, B., Thomas, R. Packing directed circuits exactly. Combinatorica 31, 397–421 (2011). https://doi.org/10.1007/s00493-011-1687-5

Download citation

Mathematics Subject Classification (2000)

  • 05C20
  • 90C47