The $f$-Factor Problem for Graphs and the Hereditary Property

by Niedermeyer and Shelah and Steffens. [NShS:557]
Archive for Math Logic, 2006
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 aleph_1 . 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 aleph_2-case.


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