Question: In the Euclidean traveling salesperson problem, cities are points in the plane and the distance between two cities is the Euclidean distance between the points

In the Euclidean traveling salesperson problem, cities are points in the plane and the distance between two cities is the Euclidean distance between the points for these cities, that is, the length of the straight line joining these points. Show that an optimal solution to the Euclidean TSP is a simple polygon, that is, a connected sequence of line segments such that no two ever cross.

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