A lower bound on the size of -vertex stable graphs

A graph G is called ( H ; k ) -vertex stable if G contains a subgraph isomorphic to H even after removing any k of its vertices. By stab ( H ; k ) we denote the minimum size among the sizes of all ( H ; k ) -vertex stable graphs. In this paper we present a general result concerning ( H ; 1 ) -vertex stable graphs. Namely, for an arbitrary graph H we give a lower bound for stab ( H ; 1 ) in terms of the order, connectivity and minimum degree of H . The bound is nearly sharp.