Geodesic
A short proof of a theorem of Kano and Yu on factors in regular graphs
The electronic journal of combinatorics, Tome 14 (2007)

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Zbl EuDML
In this note we present a short proof of the following result, which is a slight extension of a nice 2005 theorem by Kano and Yu. Let $e$ be an edge of an $r$-regular graph $G$. If $G$ has a 1-factor containing $e$ and a 1-factor avoiding $e$, then $G$ has a $k$-factor containing $e$ and a $k$-factor avoiding $e$ for every $k\in\{1,2,\ldots,r-1\}$.
DOI : 10.37236/1011
Classification : 05C70 
Lutz Volkmann. A short proof of a theorem of Kano and Yu on factors in regular graphs. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/1011
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     author = {Lutz Volkmann},
     title = {A short proof of a theorem of {Kano} and {Yu} on factors in regular graphs},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/1011},
     zbl = {1120.05073},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1011/}
}
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