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A graph G is (K_{q},k) (vertex) stable if it contains a copy of K_{q} after deleting any subset of k vertices. We show that for q >= 6 and k <= q/2 + 1 the only (K_q,k) stable graph with minimum size is isomorphic to K_{q+k}.

On $(K_{q},k)$ Stable Graphs with Small $k$