Extra Credit: Suppose you are given an undirected graph G and a specified starting node s and ending node t. The HAMILTONIAN PATH problem asks whether G contains a path beginning at s and ending at t that touches every node exactly once. The HAMILTONIAN CYCLE problem asks whether G contains a cycle that touches every node exactly once (cycles dont have starting or ending points, so s and t are not used here).

Assume that HAMILTONIAN CYCLE is NP-Complete. Prove that HAMILTONIAN PATH is NP-Complete. (Hint: Make sure you remember ALL the steps needed to show that a problem is NP-Complete. Hint #2: In class, we used HAMILTONIAN PATH to show that HAMILTONIAN CYCLE is NP-Complete. This is a different problem!)