Geodesic
Neighbor Set for the Existence of $(g,f,n)$-Critical Graphs
Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 1 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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Let $G$ be a graph of order $p$. Let $g(x)$ and $f(x)$ be two nonnegative integer-valued functions defined on $V(G)$ with $g(x)\le f(x)$ for any $x\in V(G)$. A graph $G$ is said to be $(g,f,n)$-critical if $G-N$ has a $(g,f)$-factor for each $N\subseteq V(G)$ with $|N|=n$. If $g(x)\equiv a$ and $f(x)\equiv b$ for all $x\in V(G)$, then a $(g,f,n)$-critical graph is an $(a,b,n)$-critical graph. In this paper, several sufficient conditions in terms of neighbor set for graphs to be (a; b; n)-critical or $(g,f,n)$-critical are given.
Classification : 05C70. 
@article{BMMS_2011_34_1_a3,
     author = {Hongxia Liu and Guizhen Liu},
     title = {Neighbor {Set} for the {Existence} of {\((g,f,n)\)-Critical} {Graphs}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2011},
     volume = {34},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2011_34_1_a3/}
}
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Hongxia Liu; Guizhen Liu. Neighbor Set for the Existence of \((g,f,n)\)-Critical Graphs. Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2011_34_1_a3/