Skip to main content
SpringerLink
Log in

The f-factor Problem for Graphs and the Hereditary Property

  • Published:
Archive for Mathematical Logic Aims and scope Submit manuscript

Abstract

If P is a hereditary property then we show that, for the existence of a perfect f-factor, P is a sufficient condition for countable graphs and yields a sufficient condition for graphs of size ℵ1. Further we give two examples of a hereditary property which is even necessary for the existence of a perfect f-factor. We also discuss the ℵ2-case.

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

Similar content being viewed by others

References

  1. Fodor G. (1956). Eine Bemerkung zur Theorie der regressiven Funktionen. Acta Sci. Math. (Szeged) 17:139–142

    MATH  MathSciNet  Google Scholar 

  2. Holz M., Steffens K., Weitz E. (1999). Introduction to cardinal arithmetic, Birkhäuser, Advanced Texts, Basel, Boston, Berlin

  3. Lovász, L., Plummer, M.D.: Matching theory. Ann. Discrete Math. 29, North-Holland (1986)

  4. Niedermeyer, F.: f-optimal factors of infinite graphs. Discrete Math. 95, 231-254, North Holland (1991)

  5. Tutte W.T. (1952). The factors of graphs. Can.J.Math. 4:314–328

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bonn, Germany

    Frank Niedermeyer

  2. Jerusalem, Israel

    Saharon Shelah

  3. Hannover, Germany

    Karsten Steffens

Authors
  1. Frank Niedermeyer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Saharon Shelah
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Karsten Steffens
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Karsten Steffens.

Additional information

This paper was supported by the Volkswagen Stiftung

Rights and permissions

Reprints and permissions

About this article

Cite this article

Niedermeyer, F., Shelah, S. & Steffens, K. The f-factor Problem for Graphs and the Hereditary Property. Arch. Math. Logic 45, 665–672 (2006). https://doi.org/10.1007/s00153-006-0009-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00153-006-0009-z

Keywords

Search

Navigation