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How is the graph coloring problem NP-Complete?
The Graph Coloring decision problem is np-complete, i.e, asking for existence of a coloring with less than 'q' colors, as given a coloring , it can be easily checked in polynomial time, whether or not it uses less than 'q' colors. On the other hand the Graph Coloring Optimisation problem, which aims to find the coloring with minimum colors is np-hard, because even if you are given a coloring ...