Let G be a graph with n vertices. The k-coloring problem is to decide whether the vertices of G can be labeled from the set {1, 2, ..., k} such that for every edge (v,w) in the graph, the labels of v and w are different.  Is the (n-4)-coloring problem in P or in NP? Give a formal proof for your answer.  A 'Yes' or 'No' answer is not sufficient to get a non-zero mark on this question.

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Q: Hall’s

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