Course Solutions Uncategorized (Solved) : 4 8 Points K Color Given Graph G V E K Coloring Function C V 1 2 K C U V Every Edge U V E Q30546047 . . . .

(Solved) : 4 8 Points K Color Given Graph G V E K Coloring Function C V 1 2 K C U V Every Edge U V E Q30546047 . . . .

 

4. (8 points) K-COLOR. Given a graph G (V,E), a k-coloring is a function c: V-> (1, 2,..., k) such that c(u) (v) for every edge (u,v) e E. In other words the number 1, 2, .., k represent the k colors and adjacent vertices must have different colors. The decision problems K-COLOR asks if a graph can be colored with at most K colors. 41. a. The 2-COLOR decision problem is in P. Describe an efficient algorithm to determine if a graph has a 2-coloring. What is the running time of your algorithm? b. The 3-COLOR decision problem is NP-complete by using a reduction from SAT. that 3-COLOR is NP-complete to prove that 4-COLOR is NP-complete. Use the fact

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