Given n points in the graph. Given that all distances between each two points are of different values. In graph we draw one line from each point to the nearest point. We should prove that there are no intersections.
The only things I found doesn't give me much:
a) there is at least one pair of points where there is line from A to B and from B to A;
b) I tried is to assume that there is intersection. Let us say that AB intersects with CD. We can draw some quadrilateral. Then I tried to use some triangle inequality rules, but this basically doesn't help me to prove anything.
Can you point me what else I can try to use?