The f-Factor Problem for Graphs and the Hereditary Property

Frank Niedermeyer; Saharon Shelah; Karsten Steffens

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arXiv · math/0404179

The f-Factor Problem for Graphs and the Hereditary Property

Frank Niedermeyer·Saharon Shelah·Karsten Steffens

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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 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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Frank Niedermeyer, Saharon Shelah, Karsten Steffens. 2004-04-08. The f-Factor Problem for Graphs and the Hereditary Property. https://arxiv.org/abs/math/0404179

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