An undirected graph G = (V, E) is called “k-colorable” if there exists a way to color the nodes with k colors such that no pair of adjacent nodes are assigned the same color. I.e. G is k-colorable iff there exists a k-coloring χ : V → {1, . . . , k}, such that for all (u, v) ∈ E, χ(u) ̸= χ(v) (the function χ is called a proper k-coloring). The “k-colorable problem” is the problem of determining whether an input graph G = (V, E) is k-colorable. Prove that the 3-colorable problem ≤P the 4-colorable problem.

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Q: Hall’s

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A: SUMMARY: - hence, we discussed all the points.

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A: Dear Student, The answer to your question is given below -

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