Why does TSP require no repetition of cities?
It doesn't matter exactly how you define it because it's just a way of modelling a real-world problem. In TSP, you just have a set of cities and the cost of travelling between each pair of them. That doesn't exclude the possibility that, in the real world situation you're modelling, the best route between B and&nbsp;C might go through&nbsp;A. If that was the case then, yes, the route that is modeled as ABCA in TSP may very well really involve driving through&nbsp;A an extra time on the way from B to&nbsp;C but such detail is abstracted away in the TSP model.