Packing directed circuits

Abstract

We prove a conjecture of Younger, that for every integern≥0 there exists an integert≥0 such that for every digraphG, eitherG hasn vertex-disjoint directed circuits, orG can be made acyclic by deleting at mostt vertices.

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

References

  1. [1]

    P. Erdős andL. Pósa: On the independent circuits contained in a graph,Canad. J. Math.,17 (1965), 347–352.

    Google Scholar 

  2. [2]

    P. Erdős andG. Szekeres: A combinatorial problem in geometry,Compositio Math.,2 (1935), 463–470.

    Google Scholar 

  3. [3]

    S. Fortune, J. E. Hopcroft andJ. Wyllie: The directed subgraph homeomorphism problem,J. Theoret. Comput. Sci.,10 (1980), 111–121.

    Google Scholar 

  4. [4]

    T. Gallai: Problem 6, inTheory of Graphs, Proc. Colloq. Tihany 1966 (New York), Academic Press, 1968, p.362.

  5. [5]

    W. McCuaig: Intercyclic digraphs,Graph Structure Theory, (Neil Robertson and Paul Seymour, eds.),AMS Contemporary Math.,147 (1993), 203–245.

  6. [6]

    F. P. Ramsey: On a problem of formal logic,Proc. London Math. Soc.,30 (1930), 264–286.

    Google Scholar 

  7. [7]

    P. D. Seymour: Packing directed circuits fractionally,Combinatorica,15 (1995), 281–288.

    Google Scholar 

  8. [8]

    D. H. Younger: Graphs with interlinked directed circuits,Proceedings of the Midwest Symposium on Circuit Theory,2 (1973), XVI 2.1-XVI 2.7.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Additional information

Research partially supported by DONET ECHM contract CHRXCT930090.

Research partially supported by DIMACS, by NSF grant DMS-9401981 and by ONR grant N00014-92-J-1965, and partially performed under a consulting agreement with Bellcore.

Research partially supported by DIMACS, by Université de Paris VI, by NSF grant DMS-9303761 and by ONR grant N00014-93-1-0325, and partially performed under a consulting agreement with Bellcore.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Reed, B., Robertson, N., Seymour, P. et al. Packing directed circuits. Combinatorica 16, 535–554 (1996). https://doi.org/10.1007/BF01271272

Download citation

Mathematics Subject Classification (1991)

  • 05 C 20
  • 05 C 38
  • 05 C 70