An undirected graph G = (V,E) is two colorable if each vertex x = V can be assigned one of two colors (say, black or gold) such that for every edge (u, v) EE, u and v have different colors. Use bread-first search to design an algorithm that determines whether a graph is two colorable. If the graph is indeed two colorable, your algorithm should produce the assignment of black or gold to each vertex. a. Describe your algorithm at a high-level. b. Argue that if your algorithm says G is not two colorable then there is no way to two color G. It is not sufficient to argue that your algorithm did not find a two coloring. You must argue that a two coloring is not possible. c. Argue that when your algorithm outputs a two coloring of the graph, it is indeed a legitimate two coloring. (I.e., no edge connects two gold vertices or two black vertices.) d. State and briefly justify the running time of your algorithm.