Let [n] be the set {1, 2,. . . , n}.For any a,b∈N, denote G(a,b) by a graph (not directed) defined by the following rule: the vertices have the form (i, f), where i∈[a], and f:[a]→. A vertex (i, f) and a vertex (j, g) are connected if i=j, and f(k)=g(k) holds exactly for k strictly between i and j. Prove that for any c∈N there is a,b∈N such that the vertices of G (a, b) cannot be well-colored with c colors. graph theorycombinatoricsColoring