id: 06109259 dt: j an: 06109259 au: Zhou, Sizhong; Xu, Lan; Sun, Zhiren ti: Independence number and minimum degree for fractional ID-$k$-factor-critical graphs. so: Aequationes Math. 84, No. 1-2, 71-76 (2012). py: 2012 pu: Birkhäuser Verlag (Springer), Basel la: EN cc: ut: independence number; minimum degree; fractional $k$-factor; fractional ID-$k$-factor-critical graph ci: li: doi:10.1007/s00010-012-0121-6 ab: Summary: Let $k$ be an integer with $k \geq 1$, and let $G$ be a graph. A $k$-factor of $G$ is a spanning subgraph $F$ of $G$ such that $d _{F }(x) = k$ for each ${x\in V(G)}$. Let ${h:E(G)\rightarrow[0,1]}$ be a function. If ${\sum_{e\ni x}h(e)=k}$ holds for each ${x\in V(G)}$ , then we call $G[F _{h }]$ a fractional $k$-factor of $G$ with indicator function $h$, where ${F_h=\{e\in E(G): h(e) >0 \}}$. A graph $G$ is fractional independent-set-deletable $k$-factor-critical (in short, fractional ID-$k$-factor-critical) if $G - I$ has a fractional $k$-factor for every independent set $I$ of $G$. In this paper, we prove that if ${α(G)\leq\frac{4k(δ(G)-k+1)}{k^{2}+6k+1}}$, then $G$ is fractional ID-$k$-factor-critical. The result is best possible in some sense. rv: