Near equipartitions of colored point sets

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 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.


Published in:
Computational Geometry-Theory And Applications, 65, 35-42
Year:
2017
Publisher:
Amsterdam, Elsevier Science Bv
ISSN:
0925-7721
Keywords:
Laboratories:




 Record created 2017-09-05, last modified 2018-09-13


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