A k-colored graph is an undirected graph G = (V;E) where each edge is assigned one of the k colors from 1; :::; k.

A path from vetex u to vertex v in G is called bichromatic if the edges in the path use at most 2 of the k colors. 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 bichromatic path from u to v in G and analyze the time complexity of your algorithm in terms of |V|; |E| and k