On the existence of edge cuts leaving several large components

We characterize graphs of large enough order or large enough minimum degree which contain edge cuts whose deletion results in a graph with a specified number of large components. This generalizes and extends recent results due to Ou [Jianping Ou, Edge cuts leaving components of order at least m , Discrete Math. 305 (2005), 365–371] and Zhang and Yuan [Z. Zhang, J. Yuan, A proof of an inequality concerning k -restricted edge connectivity, Discrete Math. 304 (2005), 128–134].