Further consequences of the colorful helly hypothesis

Leonardo Martínez-Sandoval, Edgardo Roldán-Pensado, Natan Rubin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


Let F be a family of convex sets in ℝd, which are colored with d + 1 colors. We say that F satisfies the Colorful Helly Property if every rainbow selection of d + 1 sets, one set from each color class, has a non-empty common intersection. The Colorful Helly Theorem of Lovász states that for any such colorful family F there is a color class F i ⊂ F, for 1 ≤ i ≤ d +1, whose sets have a non-empty intersection. We establish further consequences of the Colorful Helly hypothesis. In particular, we show that for each dimension d ≥ 2 there exist numbers f(d) and g(d) with the following property: either one can find an additional color class whose sets can be pierced by f(d) points, or all the sets in F can be crossed by g(d) lines.

Original languageEnglish
Title of host publication34th International Symposium on Computational Geometry, SoCG 2018
EditorsCsaba D. Toth, Bettina Speckmann
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Number of pages5324
ISBN (Electronic)9783959770668
StatePublished - 1 Jun 2018
Event34th International Symposium on Computational Geometry, SoCG 2018 - Budapest, Hungary
Duration: 11 Jun 201814 Jun 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference34th International Symposium on Computational Geometry, SoCG 2018


  • Colorful Helly-type theorems
  • Convex sets
  • Geometric transversals
  • Line transversals
  • Transversal numbers
  • Weak epsilon-nets

ASJC Scopus subject areas

  • Software


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