The edge deletion problem (EDP) corresponding to a given class H of graphs is to find the minimum number of edges whose deletion from a given graph G results in a subgraph G', G' - H. In this paper we extend previous complexity results by showing that the EDP corresponding to any class H of graphs in each of the following cases is NP-hard. (i) H is defined by a set of forbidden homeomorphs or minors in which every member is a 2-connected graph with minimum degree 3. (ii) H is defined by K4 — e as a forbidden homeomorph or minor. (iii) H is defined by Pl, l - 3, the simple path on l nodes, as a forbidden induced subgraph.
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