Geodesic
Pan-factorial property in regular graphs
The electronic journal of combinatorics, Tome 12 (2005)

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Zbl EuDML
Among other results, we show that if for any given edge $e$ of an $r$-regular graph $G$ of even order, $G$ has a 1-factor containing $e$, then $G$ has a $k$-factor containing $e$ and another one avoiding $e$ for all $k$, $1 \leq k \leq r-1$.
DOI : 10.37236/1990
Classification : 05C70, 05C75 
M. Kano; Qinglin Yu. Pan-factorial property in regular graphs. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1990
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     author = {M. Kano and Qinglin Yu},
     title = {Pan-factorial property in regular graphs},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1990},
     zbl = {1079.05075},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1990/}
}
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