In this note, we disprove the long-standing conjecture that any complete geometric graph on $2n$ vertices can be partitioned into $n$ plane spanning trees. Despite several approaches this conjecture remained open to date. We provide a family of counterexamples based on so-called bumpy wheel sets. To this end, we will give two proofs --- one that is computer assisted (based on an ILP formulation) and a pure pen and paper proof.

翻译：在本说明中,我们反驳了长期的推测,即任何关于$2n美元脊椎的完整的几何图都可分割成一整架飞机横贯树木。尽管这一推测迄今仍然有好几种办法。我们提供一套基于所谓颠簸轮椅的反抽样。为此,我们将提供两个证据 -- -- 一个是计算机辅助的(以ILP配方为基础),另一个是纯笔和纸的证明。