A Hamiltonian cycle in graph \(\mathbf{G}\) is a cycle that visits every vertex in the graph exactly once before returning to the start vertex. The problem HAMILTONIAN CYCLE asks whether graph \(\mathbf{G}\) does in fact contain a Hamiltonian cycle. Assuming that HAMILTONIAN CYCLE is \(\mathcal{N P}\)-complete, prove that the decision-problem form of TRAVELING SALESMAN is \(\mathcal{N} \mathcal{P}\)-complete.