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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.
f(k, m) = Θ(k 3). Furthermore we give a construction which does not contain an empty rainbow quadrilateral.
| Original language | English |
|---|---|
| Pages | 38:1 |
| Number of pages | 38 |
| Publication status | Published - 2020 |
| Event | 36th European Workshop on Computational Geometry : EuroCG 2020 - University of Würzburg, Würzburg, Virtuell, Germany Duration: 16 Mar 2020 → 18 Mar 2020 https://www1.pub.informatik.uni-wuerzburg.de/eurocg2020/ |
Conference
| Conference | 36th European Workshop on Computational Geometry |
|---|---|
| Abbreviated title | EuroCG 2020 |
| Country/Territory | Germany |
| City | Würzburg, Virtuell |
| Period | 16/03/20 → 18/03/20 |
| Internet address |
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Dive into the research topics of 'Empty Rainbow Triangles in k-colored Point Sets'. Together they form a unique fingerprint.Activities
- 1 Conference or symposium (Participation in/Organisation of)
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36th European Workshop on Computational Geometry
Daniel Perz (Participant)
16 Mar 2020 → 18 Mar 2020Activity: Participation in or organisation of › Conference or symposium (Participation in/Organisation of)