Holmsen, Andreas E.Kyncl, JanValculescu, Claudiu2017-09-052017-09-052017-09-05201710.1016/j.comgeo.2017.05.001https://infoscience.epfl.ch/handle/20.500.14299/140037WOS:000406734200004Suppose 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 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. (C) 2017 Elsevier B.V. All rights reserved.Colored point setConvex equipartitionColorful islandHam sandwich theoremtext::journal::journal article::research article