How do I do this?  We say a graph G = (V, E) has a k-coloring for some positive integer k if we can assign k different colors to vertices of G such that for every edge (v, w) ∈ E, the color of v is different to the color w. More formally, G = (V, E) has a k-coloring if there is a function f : V → {1, 2, . . . , k} such that for every (v, w) ∈ E, f(v) 6= f(w). 3-Color problem is defined as follows: Given a graph G = (V, E), does it have a 3-coloring? 4-Color problem is defined as follows: Given a graph G = (V, E), does it have a 4-coloring? Prove that 3-Color ≤P 4-Color. (hint: add vertex to 3-Color problem instance.)

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

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