I know that graph contractability is NP-complete. To be specific given G=(V1,E1) and H=(V2,E2), can a graph isomorphic to H be obtained from G by a sequence of edge contractions ? However my problem is a little bit different from the traditional graph contractability. In the traditional graph contractability problem we contract the original graph by different sequences of edge mergings. However in my problem after one edge is picked and merged, some edges are excluded from further merging. Any hint on whether this problem is NP-complete or not. If so any hint on how to prove it ?