Pan-Factorial Property in Regular Graphs

M. Kano, Qinglin Yu

Abstract


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 $k$, $1 \leq k \leq r-1$.


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