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\iteman{io-port 06107209}
\itemau{Zhou, Sizhong; Xu, Zurun; Zong, Minggang}
\itemti{Some new sufficient conditions for graphs to be $(a,b,k)$-critical graphs.}
\itemso{Ars Comb. 102, 11-20 (2011).}
\itemab
Summary: Let $G$ be a graph, and let $a,b$ and $k$ be nonnegative integers with $1\leq a\leq b$. An $[a,b]$-factor of graph $G$ is defined as a spanning subgraph $F$ of $G$ such that $a\leq d_{F}(x)\leq b$ for each $x\in V(G)$. Then a graph $G$ is called an $(a,b,k)$-critical graph if after any $k$ vertices of $G$ are deleted the remaining subgraph has an $[a,b]$-factor. In this paper three sufficient conditions for graphs to be $(a,b,k)$-critical graphs are given. Furthermore, it is shown that the results in this paper are best possible in some sense.
\itemrv{~}
\itemcc{}
\itemut{graph; stability number; degree condition; neighborhood union; $[a,b]$-factor, $(a,b,k)$-critical graph}
\itemli{}
\end