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: