Packing Plane Spanning Trees into a Point Set
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Let P be a set of n points in the plane in general position. We show that at least n/3 plane spanning trees can be packed into the complete geometric graph on P. This improves the previous best known lower bound Ω(√(n)). Towards our proof of this lower bound we show that the center of a set of points, in the d-dimensional space in general position, is of dimension either 0 or d.
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