Prove that 3-COL poly Independent set, demonstrate that the independent set is NP-competent. (Hint: Consider the combination u, c, where u is a G3-COL node and c is a colour, as a 3-coloring for the graph G3-COL. A portion of the vertices in the graph GInd are chosen by an independent set. Therefore, a node would be needed for each pair of u and c in order to build the graph Gind in the instance GInd, NInd = InstanceMap(G3-COL). A valid 3-coloring of the original graph must match to each valid independent set of size n in the constructed graph, so take care when defining the edges for the graph GInd = InstanceMap(G3-COL). If a surprising number of independent sets appear in the created graph

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