  Suppose that $nk$ points in general position in the plane are colored red and
blue, with at least $n$ points of each color. We show that then there exist $n$
pairwise disjoint convex sets, each of them containing $k$ of the points, and
each of them containing points of both colors. We also show that if $P$ is a
set of $n(d+1)$ points in general position in $\mathbb{R}^d$ colored by $d$
colors with at least $n$ points of each color, then there exist $n$ pairwise
disjoint $d$-dimensional simplices with vertices in $P$, each of them
containing a point of every color. These results can be viewed as a step
towards a common generalization of several previously known geometric
partitioning results regarding colored point sets.
