On the asymptotic growth rate of some spanning trees embedded in Rd

We show that, for an Euclidean minimal k-insertion tree (EMITk) with n vertices, if the weight w of an edge e is its Euclidean length to the power of α, ∑e∈EMITkw(e) is O(n⋅k−α/d) in the worst case, where d is the dimension, for d≥2 and 0<α0.