A neighbourhood condition for graphs to have \([a,b]\)-factors
Let \(a\) and \(b\) be integers such that \(1\leq a\leq b\). An \([a,b]\)-factor of a graph \(G\) is defined as a spanning subgraph \(F\) of \(G\) such that \(a\leq\deg_F(x)\leq b\) for all vertices \(x\). The note shows that \(G\) has an \([a,b]\)-factor if the minimum degree \(\delta(x)\geq a\), \(n\geq 2(a+b)(a+ b-1)/b\) and \(|N_G(x)\cup N_G(y)|\geq an/(a+ b)\) for any two non-adjacent vertices \(x\) and \(y\) of \(G\).
scientific article; zbMATH DE number 1533357