\input zb-basic
\input zb-ioport
\iteman{io-port 06090579}
\itemau{Tang, Siping; Li, Jianxiang; Gao, Mingke; Hu, Xing}
\itemti{$[a,b]$-factors containing a given $k$-regular subgraph.}
\itemso{Acta Math. Appl. Sin. 34, No. 6, 1032-1045 (2011).}
\itemab
Summary: Let $G$ be a graph, and let $n, k, r, a$ and $b$ be integers such that $k\geq 1,\ k\leq a<b$ and $n\geq 3$. For given $k$-regular subgraph $H$ of $G$, if $G$ is $K_{1,n}$-free and the minimum degree of $G$ is at least $$\left (\frac{n (a+1)+b-a- (k+1)}{b-k}\right)\left\lceil\frac{an+b-a-k}{2 (n-1)}\right\rceil-\frac{n-1}{b-k}\left (\left\lceil\frac{an+b-a-k}{2 (n-1)}\right\rceil\right)^2-1,$$ then $G$ has an $[a, b]$-factor $F$ such that $E (H)\subseteq E (F)$. Similarly, we also obtain a degree condition for graphs to have an $r$-factor containing a given $k$-regular subgraph of $G$. Furthermore, it is shown that the degree conditions are sharp.
\itemrv{~}
\itemcc{}
\itemut{$k$-regular graph; $r$-factor; $[a,b]$-factor; degree condition}
\itemli{}
\end