Note on the factors of graphs


Dǎnuţ Marcu




We show that if $G$ is a connected graph of order at least four with an 1-factor $F$, and $k$ a positive integer such that $G-V(e)$ has a $k$-factor for each $e\in F$, then $G$ has a $k$-factor, where $V(e)$ denotes the set of endvertices of edge $e$.