A neighborhood condition for graphs to have \([a,b]\)-factors excluding a given subgraph (Q2811824)

For a graph \(G\) and two positive integers \(a\leq b\), a graph \(F\) is an \([a,b]\)-factor of \(G\) if \(F\) is a spanning subgraph of \(G\) with minimum degree \(\delta (F)\geq a\) and maximum degree \(\Delta (F)\leq b\). In this paper, it is proven that in a graph \(G\) of order \(n\) and minimum degree \(\delta (G)\geq a+2m\), if \(|N_G(x)\cup N_G(y)|\geq {{an}\over {a+b}}\) for any two non-adjacent vertices \(x\) and \(y\) in \(G\) such that \(N_G(x)\cap N_G(y)\not=\emptyset\), then \(G\) has an \([a,b]\)-factor that excludes any set of \(m\) edges in \(G\).