Recently, the second and third author showed that complete geometric graphs on $2n$ vertices in general cannot be partitioned into $n$ plane spanning trees. Building up on this work, in this paper, we initiate the study of partitioning into beyond planar subgraphs, namely into $k$-planar and $k$-quasi-planar subgraphs and obtain first bounds on the number of subgraphs required in this setting.

翻译：最近,第二和第三作者指出,一般而言,$2,000美元的脊椎上的完整几何图无法分割成一整平面横扫树木。 本文以这项工作为基础,开始研究将2,500美元和1,500美元之间的平面分图分割成平面以外的分层,即平面和平面分图,并获得这一设置所需的分层数的首选界限。