Given a graph G = (V;E) an almost independent set I  V is a generalization of an independent set where each vertex u 2 I is connected to at most one other vertex in I but no more. In other words for all u; v 2 I if (u; v) 2 E then (u; z) =2 E for all z 2 I (equvalently (v; z) =2 E). Note that every independent set is also almost independent. Prove that the problem of  nding whether there exists an almost independent set of size k for some k, is NP-complete.

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A:

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