Sufficient conditions for restricted-edge-connectivity to be optimal

For a connected graph G=(V,E), an edge set S@?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 minimum k-restricted-edge-cut is the k-restricted-edge-connectivity of G, denoted by @l"k(G). In this paper, we study sufficient conditions for @l"k(G) to be optimal, especially when k=2 and 3.

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