Sufficient conditions for restricted-edge-connectivity to be optimal

For a connected graph G=(V,E)G=(V,E), an edge set S⊂ES⊂E is a k  -restricted-edge-cut if G-SG-S is disconnected and every component of G-SG-S has at least k vertices. The cardinality of a minimum k-restricted-edge-cut is the k-restricted-edge-connectivity of G  , denoted by λk(G)λk(G). In this paper, we study sufficient conditions for λk(G)λk(G) to be optimal, especially when k=2k=2 and 3.