A \emph{complete geometric graph} consists of a set $P$ of $n$ points in the plane, in general position, and all segments (edges) connecting them. It is a well known question of Bose, Hurtado, Rivera-Campo, and Wood, whether there exists a positive constant $c<1$, such that every complete geometric graph on $n$ points can be partitioned into at most $cn$ plane graphs (that is, noncrossing subgraphs). We answer this question in the affirmative in the special case where the underlying point set $P$ is \emph{dense}, which means that the ratio between the maximum and the minimum distances in $P$ is of the order of $\Theta(\sqrt{n})$.

翻译：一个\emph{完全几何图}由平面上一般位置的$n$个点集$P$及其所有连接线段（边）构成。Bose、Hurtado、Rivera-Campo和Wood提出的著名问题是：是否存在正常数$c<1$，使得任意$n$点完全几何图都能被划分为至多$cn$个平面图（即非交叉子图）。本文在底层点集$P$为\emph{稠密}的特殊情况下肯定地回答了该问题，这意味着$P$中最大与最小距离之比为$\Theta(\sqrt{n})$量级。