# Sh:557

- Niedermeyer, F., Shelah, S., & Steffens, K. (2006).
*The f-factor problem for graphs and the hereditary property*. Arch. Math. Logic,**45**(6), 665–672. arXiv: math/0404179 DOI: 10.1007/s00153-006-0009-z MR: 2252248 -
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. - published version (8p)

Bib entry

@article{Sh:557, author = {Niedermeyer, Frank and Shelah, Saharon and Steffens, Karsten}, title = {{The $f$-factor problem for graphs and the hereditary property}}, journal = {Arch. Math. Logic}, fjournal = {Archive for Mathematical Logic}, volume = {45}, number = {6}, year = {2006}, pages = {665--672}, issn = {0933-5846}, doi = {10.1007/s00153-006-0009-z}, mrclass = {05C70 (03E10)}, mrnumber = {2252248}, mrreviewer = {Lutz Volkmann}, doi = {10.1007/s00153-006-0009-z}, note = {\href{https://arxiv.org/abs/math/0404179}{arXiv: math/0404179}}, arxiv_number = {math/0404179} }