  A \emph{geometric graph} is a graph whose vertex set is a set of points in
general position in the plane, and its edges are straight line segments joining
these points. We show that for every integer $k \ge 2$, there exists a constat
$c>0$ such that the following holds. The edges of every dense geometric graph
can be colored with $k$ colors, such that the number of pairs of edges of the
same color that cross is at most $(1/k-c)$ times the total number of pairs of
edges that cross. The case when $k=2$ and $G$ is a complete geometric graph,
was proved by Aichholzer et al.[\emph{GD} 2019].
