A k-colored graph is an undirected graph G = (V;E) where each edge is assigned one of the k colors from 1; :::; k. (i) A path from veterx u to vertex v in G is called monochromatic if all the edges in the path have the same color. Given a k-colored graph G = (V;E) and a pair of vertices (u; v), provide an efficient algorithm to determine whether there is a monochromatic path from u to v in G and analyze the time complexity of your algorithm in terms of |V |; |E| and k.