Let P be a set of n points in the plane in general position. We show that at least $\lfloor n/3\rfloor$ plane spanning trees can be packed into the complete geometric graph on P. This improves the previous best known lower bound $\mathrm{\Omega }\left(\sqrt{n}\right)$. 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.

中文翻译：

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将生成树的平面打包到一个点集中

令P为平面中一般位置上的n个点的集合。我们证明至少$\lfloor ñ/3\rfloor$可以将平面生成树打包成P上的完整几何图。这改善了先前最著名的下限$\mathrm{\Omega }（\sqrt{ñ}）$。为了证明这一下界，我们表明在一般位置的d维空间中，一组点的中心的维数为0或d。