Empty Rainbow Triangles in k-colored Point Sets

Ruy Fabila-Monroy, Daniel Perz, Ana Laura Trujillo

Publikation: KonferenzbeitragPaper

Abstract

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.
Originalspracheenglisch
Seiten38:1
Seitenumfang38
PublikationsstatusVeröffentlicht - 2020
Veranstaltung36th European Workshop on Computational Geometry - University of Würzburg, Virtuell, Deutschland
Dauer: 16 März 202018 März 2020
https://www1.pub.informatik.uni-wuerzburg.de/eurocg2020/

Konferenz

Konferenz36th European Workshop on Computational Geometry
KurztitelEuroCG 2020
Land/GebietDeutschland
OrtVirtuell
Zeitraum16/03/2018/03/20
Internetadresse

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