Volume 34 • Number 1 • 2011   • Neighbor Set for the Existence of \((g,f,n)\)-Critical Graphs Hongxia Liu and Guizhen Liu Abstract. 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. 2010 Mathematics Subject Classification: 05C70. Full text: PDF