Empty rainbow triangles in k-colored point sets

Ruy Fabila-Monroy*, Daniel Perz, Ana Laura Trujillo-Negrete

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number101731
JournalComputational Geometry: Theory and Applications
Publication statusPublished - Apr 2021


  • Empty triangles
  • Erdős-Szekeres
  • k-holes

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics


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