Minimal TSP Tour is coNP-Complete

The problem of deciding if a Traveling Salesman Problem (TSP) tour is minimal was proved to be coNP–complete by Papadimitriou and Steiglitz. We give an alternative proof based on a polynomial time reduction from 3SAT. Like the original proof, our reduction also shows that given a graph G and an Hamiltonian path of G, it is NP–complete to check if G contains an Hamiltonian cycle (Restricted Hamiltonian Cycle problem).