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A graph G is called (H;k)-vertex stable if G contains a subgraph isomorphic to H ever after removing any of its k vertices. Q(H;k) denotes the minimum size among the sizes of all (H;k)-vertex stable graphs. In this paper we complete the characterization of -vertex stable graphs with minimum size. Namely, we prove that for m ≥ 2 and n ≥ m+2, and as well as are the only -vertex stable graphs with minimum size, confirming the conjecture of Dudek and Zwonek.
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