Minimally 3-restricted edge connected graphs

For a connected graph G=(V,E), an edge set S@?E is a 3-restricted edge cut if G-S is disconnected and every component of G-S has order at least three. The cardinality of a minimum 3-restricted edge cut of G is the 3-restricted edge connectivity of G, denoted by @l"3(G). A graph G is called minimally 3-restricted edge connected if @l"3(G-e)<@l"3(G) for each edge e@?E. A graph G is @l"3-optimal if @l"3(G)=@x"3(G), where @x"3(G)=max{@w(U):U@?V(G),G[U] is connected,|U|=3}, @w(U) is the number of edges between U and V@?U, and G[U] is the subgraph of G induced by vertex set U. We show in this paper that a minimally 3-restricted edge connected graph is always @l"3-optimal except the 3-cube.