Coloring Delaunay-edges and their generalizations

Eyal Ackerman, Balázs Keszegh, Dömötör Pálvölgyi

Research output: Contribution to journalArticlepeer-review


We consider geometric hypergraphs whose vertex set is a finite set of points (e.g., in the plane), and whose hyperedges are the intersections of this set with a family of geometric regions (e.g., axis-parallel rectangles). A typical coloring problem for such geometric hypergraphs asks, given an integer k, for the existence of an integer m=m(k), such that every set of points can be k-colored such that every hyperedge of size at least m contains points of different (or all k) colors. We generalize this notion by introducing coloring of t-subsets of points such that every hyperedge that contains enough points contains t-subsets of different (or all) colors. In particular, we consider all t-subsets and t-subsets that are themselves hyperedges. The latter, with t=2, is equivalent to coloring the edges of the so-called Delaunay-graph. In this paper we study colorings of Delaunay-edges with respect to halfplanes, pseudo-disks, axis-parallel and bottomless rectangles, and also discuss colorings of t-subsets of geometric and abstract hypergraphs, and connections between the standard coloring of vertices and coloring of t-subsets of vertices.

Original languageEnglish
Article number101745
JournalComputational Geometry: Theory and Applications
StatePublished - Jun 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier B.V.


  • Delaunay-edges
  • Delaunay-graph
  • Geometric hypergraphs

ASJC Scopus subject areas

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


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