Abstract
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 Rd 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.
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