Skip to main content
Log in

Hall's criterion as a ‘self-refining’ result

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

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.

References

  1. Hall, P.: On representatives of subsets. J. London Math. Soc.10, 26–30 (1935).

    Google Scholar 

  2. Halmos, P. R. andH. E. Vaughan: The marriage problem. Amer. J. Math.72, 214–215 (1950).

    Google Scholar 

  3. Higgins, P. J.: Disjoint transversals of subsets. Canad. J. Math.11, 280–285 (1959).

    Google Scholar 

  4. Hoffman, A. J. andH. W. Kuhn: Systems of distinct representatives and linear programming. Amer. Math. Monthly63, 455–460 (1956).

    Google Scholar 

  5. Mendelsohn, N. S. andA. L. Dulmage: Some generalizations of the problem of distinct representatives. Canad. J. Math.10, 230–241 (1958).

    Google Scholar 

  6. Mirsky, L.: Transversals of subsets. Quart. J. Math. (Oxford) (2)17, 58–60 (1966).

    Google Scholar 

  7. Mirsky, L. andHazel Perfect: Systems of representatives. J. Math. Analysis Appl.15, 520–568 (1966).

    Google Scholar 

  8. Mirsky, L. andHazel Perfect: Applications of the notion of independence to problems of combinatorial analysis. J. Combinatorial Theory2, 327–357 (1967).

    Google Scholar 

  9. Ore, O.: Graphs and matching theorems. Duke Math. J.22, 625–639 (1955).

    Google Scholar 

  10. Perfect, Hazel: Symmetrized form of P. Hall's theorem on distinct representatives. Quart. J. Math. (Oxford) (2)17, 303–306 (1966).

    Google Scholar 

  11. Perfect, Hazel, andJ. S. Pym: An extension of Banach's mapping theorem, with applications to problems concerning common representatives. Proc. Cambridge Phil. Soc.62, 187–192 (1966).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mirsky, L. Hall's criterion as a ‘self-refining’ result. Monatshefte für Mathematik 73, 139–146 (1969). https://doi.org/10.1007/BF01303662

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01303662

Navigation