### 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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