Some results on \((g,f)\)-uniform graphs (Q2839678)

Let \(g\) and \(f\) be nonnegative integer-valued functions defined on the vertex set of a graph \(G\), such that \(0\leq g(x)\leq f(x)\) for every \(x\in V(G)\). The degree of a vertex \(x\in V(G)\) is denoted by \(d_G(x)\). A \((g,f)\)-factor is a spanning subgraph \(F\) such that \(g(x)\leq d_F(x)\leq f(x)\) for all \(x\in V(G)\). \(G\) is \textit{\((g,f)\)-uniform} if, for every \(e\in E(G)\), there exists one \((g,f)\)-factor containing \(e\) and another excluding \(e\). From the authors' abstract: ``In this paper some sufficient conditions for a graph to be a \((g,f)\)-uniform graph are given and discussed.''