Archive for Mathematical Logic

, Volume 45, Issue 6, pp 665–672 | Cite as

The f-factor Problem for Graphs and the Hereditary Property

  • Frank Niedermeyer
  • Saharon Shelah
  • Karsten SteffensEmail author


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.


Bipartite Graph Discrete Math Greek Letter Complete Bipartite Graph Factor Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Fodor G. (1956). Eine Bemerkung zur Theorie der regressiven Funktionen. Acta Sci. Math. (Szeged) 17:139–142zbMATHMathSciNetGoogle Scholar
  2. 2.
    Holz M., Steffens K., Weitz E. (1999). Introduction to cardinal arithmetic, Birkhäuser, Advanced Texts, Basel, Boston, BerlinGoogle Scholar
  3. 3.
    Lovász, L., Plummer, M.D.: Matching theory. Ann. Discrete Math. 29, North-Holland (1986)Google Scholar
  4. 4.
    Niedermeyer, F.: f-optimal factors of infinite graphs. Discrete Math. 95, 231-254, North Holland (1991)Google Scholar
  5. 5.
    Tutte W.T. (1952). The factors of graphs. Can.J.Math. 4:314–328zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Frank Niedermeyer
    • 1
  • Saharon Shelah
    • 2
  • Karsten Steffens
    • 3
    Email author
  1. 1.BonnGermany
  2. 2.JerusalemIsrael
  3. 3.HannoverGermany

Personalised recommendations