Sufficient conditions for restricted-edge-connectivity to be optimal (Q2461216)

For a connected graph \(G= (V,E)\), an edge set \(S\subset E\) is a \(k\)-restricted-edge-cut if \(G- S\) is disconnected and every component of \(G- S\) has at least \(k\) vertices. The cardinality of a minimal \(k\)-restricted-edge-cut is the \(k\)-restricted-edge-connectivity of \(G\), denoted by \(\lambda_k(G)\). Sufficient conditions for \(\lambda_k(G)\) to be optimal are studied, especially when \(k= 2\) and \(3\).