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Euclidean Minimum Spanning Trees Restricted to One Vertex Per Grid Cell

Given an $n \times n$ grid with unit grid cells, and one point from the interior of each cell, what is are best possible lower and upper bounds for lengths of minimum spanning trees? The lower bound ...
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How to estimate the probability of an edge appearing in the minimum spanning tree of a graph?

I've been running into this problem recently and I've been stuck on it for a while. I have a set of vertices $G$ that form a complete graph. From this I need to sample $k$ vertices (which would also ...
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