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A graph G is called an (n,k)-graph if k(G- S) = n - |S| for any S C V(G) with |S| ≤ k,where k(G) denotes the connectivity of G. Mader conjectured that for k ≥ 3 the graph K2k+2-(1-factor) isthe unique (2k, k)-graph. Kriesell has settled two special cases