Travelling salesperson problem

Imagine you had to plan the tour for the Olympic Torch. Is there an efficient way of choosing the shortest possible route?

A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?

The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?