Empty Rainbow Triangles in k-colored Point Sets

Ruy Fabila-Monroy, Daniel Perz, Ana Laura Trujillo

Research output: Contribution to conferencePaper


Let S be a set of n points in general position in the plane. Suppose that each point of S has been assigned one of k ≥ 3 possible colors and that there is the same number, m, of points of each color class, so n = km. A triangle with vertices on S is empty if it does not contain points of S in its interior and it is rainbow if all its vertices have different colors. Let f(k, m) be the minimum number of empty rainbow triangles determined by S. In this paper we show that
f(k, m) = Θ(k 3). Furthermore we give a construction which does not contain an empty rainbow quadrilateral.
Original languageEnglish
Number of pages38
Publication statusPublished - 2020
Event36th European Workshop on Computational Geometry - University of Würzburg, Virtuell, Germany
Duration: 16 Mar 202018 Mar 2020


Conference36th European Workshop on Computational Geometry
Abbreviated titleEuroCG 2020
Internet address


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