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.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2017-10
Language
English
Keywords

BALANCED CONVEX PARTITIONS; PLANE; SUBDIVISIONS; THEOREM

Citation

COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, v.65, pp.35 - 42

ISSN
0925-7721
DOI
10.1016/j.comgeo.2017.05.001
URI
http://hdl.handle.net/10203/225586
Appears in Collection
MA-Journal Papers(저널논문)
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