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Given the following definitions:

  • 1) A subgraph G' of a graph G consists of a

subset of vertices and edges of G. A subgraph G' is complete if there is an edge between any pair of vertices of G'.

  • 2) An independent set of vertices of a graph G is defined as a set of vertices of G such that there is no edge between any two vertices of S.
  • Show that finding a complete subgraph of G with k vertices is NP-complete by reducing from the q-Indepedent Set problem (i.e., finding an independent set with q vertices).

    Note: you should first present the problem in its decision version and then prove the NP-completeness.

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