3. Let k0 be a fixed integer. (a) Describe an efficient algorithm that decides whether or not a given connected directed graph D admits a homomorphism to Pk, the directed path of length k. Here and elsewhere, efficient means that the number of steps taken by the algorithm is bounded by a polynomial function of the number of vertices of the given directed graph D. (A directed graph is connected if its underlying graph is connected.) (b) Prove that there is a homomorphism of D to Pk if and only if no oriented path of net length k+1 admits a homomorphism to D