Noun
subtour (plural subtours)
(graph theory) A tour that makes up part of a larger tour.
To prove that every feasible solution contains only one closed sequence of cities, it suffices to show that every subtour in a feasible solution passes through city 0 (noting that the equalities ensure there can only be one such tour). Source: Internet
For if we sum all the inequalities corresponding to for any subtour of k steps not passing through city 0, we obtain: : which is a contradiction. Source: Internet