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Question:

how are the vertex degrees of MSTs of the corresponding points that are uniformly and independently distributed in a square region of the euclidean plane and the edges being weighted with the euclidean distance between the points that are associated with the adjacent vertices?

I am especially interested in knowing the expected relative multiplicity of the leaf nodes.
Results related to other kinds of regions (e.g. disks) or other point distributions would also be interesting to know.

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  • $\begingroup$ This question is vaguely worded. What do you mean the points are iid? Do you mean the location that each point shows up at in the square is uniformly distributed, and that the locations that the points show up are mutually independent? $\endgroup$
    – Mike
    May 24, 2018 at 17:01
  • $\begingroup$ @Mike yes, you are right; I will edit accordingly. $\endgroup$
    – Manfred Weis
    May 25, 2018 at 4:30

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The article The random minimal spanning tree in high dimensions addresses my question.

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