Empty rainbow triangles in k-colored point sets

Ruy Fabila-Monroy, Daniel Perz, Ana Laura Trujillo

Publikation: Beitrag in einer FachzeitschriftArtikelBegutachtung

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. This means n=km. A polygon 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 give tight asymptotic bounds for this function. Furthermore, we show that S may not determine an empty rainbow quadrilateral for some arbitrarily large values of k and m.

Originalspracheenglisch
Aufsatznummer101731
FachzeitschriftComputational Geometry
Jahrgang95
DOIs
PublikationsstatusVeröffentlicht - Apr. 2021

ASJC Scopus subject areas

  • Computational Mathematics
  • Steuerung und Optimierung
  • Geometrie und Topologie
  • Angewandte Informatik
  • Theoretische Informatik und Mathematik

Fingerprint

Untersuchen Sie die Forschungsthemen von „Empty rainbow triangles in k-colored point sets“. Zusammen bilden sie einen einzigartigen Fingerprint.

Dieses zitieren