4. [12 points] Consider the following map coloring problem, where each region of the map must be colored one of {R, G, B, Y), and no neighboring regions may have the same color. Furthermore, we require that node C be green (G); that nodes W1, W2, W3 may not be colored red (R); and that nodes L1, L2, L3 may not be colored blue (B). L2 W1 L1 W2 L3 W3 a. Draw a constraint network(graph) corresponding to this problem. Describe the problem space in terms of Variables, Domain and constraints b. Is the network arc consistent? Prove that it is, or make it arc consistent. c. Give the variable orderings that would be selected by the following methods. Break ties in alphanumeric order. i. the minimum remaining values (MRV) heuristic ii. the degree (or "most constraining variable") heuristic d. Give a solution to the problem.