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Homework Statement
Let us have ##n \geq 3## points in a square whose side length is ##1##. Prove that there exists a graph with these points such that ##G## is connected, and
$$\sum_{\{v_i,v_j\} \in E(G)}{|v_i - v_j|} \leq 10\sqrt{n}$$
Prove also the ##10## in the inequality can't be replaced with ##1##.
Homework Equations
These may be relevant:
https://en.wikipedia.org/wiki/Trave..._length_for_random_sets_of_points_in_a_square
https://math.stackexchange.com/ques...istance-between-two-random-points-in-a-square