Given the minimum Hamiltonian path (or traveling salesman tour) H0 in an undirected weighted graph, the sensitivity analysis problem consists in finding by how much each edge weight can be perturbed individually without changing the optimality of H0. The maximum increment and decrement of the edge weight that preserve the optimality of H0 is called edge tolerance with respect to the solution H0. A method of computing lower bounds of edge tolerances based on solving the sensitivity analysis problem for appropriate relaxations of the minimum Hamiltonian path and traveling salesman problems is presented.
