Geodesic
(H,k) stable bipartite graphs with minimum size
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 573-581 Cet article a éte moissonné depuis la source Library of Science

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Let us call a graph G(H;k) vertex stable if it contains a subgraph H after removing any of its k vertices. In this paper we are interested in finding the (K_n,n+1;1) (respectively (K_n,n;1)) vertex stable graphs with minimum size.
Keywords: graph, vertex stable graph 
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Dudek, Aneta; Zwonek, Małgorzata. (H,k) stable bipartite graphs with minimum size. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 573-581. http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a8/

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[3] I. Horváth and G.Y. Katona, Extremal stable graphs, submitted.