Question: 8. (10 points) NP-Complete Problems (a) (5 points) Consider the following problem: given a graph, determine whether it can be colored using exactly 4 colors.

8. (10 points) NP-Complete Problems (a) (5 points) Consider the following

8. (10 points) NP-Complete Problems (a) (5 points) Consider the following problem: given a graph, determine whether it can be colored using exactly 4 colors. Prove that this coloring problem is NP-Complete. (b) (5 points) Prove that for all k > 4, determining whet her a graph can be colored using exactly k colors is NP-Complete

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