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The complexity of some edge deletion problems

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2 Author(s)
El-Mallah, E.S. ; Waterloo Univ., Ont., Canada ; Colbourn, C.J.

The edge deletion problem (EDP) corresponding to a given class H of graphs is to find the minimum number of edges the deletion of which from a given graph G results in a subgraph G', G '∈H. Previous complexity results are extended by showing that the EDP corresponding to any class H of graphs in each of the following cases is NP-hard. (1) H is defined by a set of forbidden homeomorphs or minors in which every member is a 2-connected graph with minimum degree three; (2) BH is defined by K4-e as a forbidden homeomorph or minor; and (3) H is defined by Pl , l⩾3, the simple path on l nodes, as a forbidden induced subgraph

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Circuits and Systems, IEEE Transactions on  (Volume:35 ,  Issue: 3 )