Discrete and lexicographic Helly-type theorems

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4 Scopus citations


Helly's theorem says that if every d+1 elements of a given finite set of convex objects in ℝd have a common point, then there is a point common to all of the objects in the set. We define three new types of Helly theorems: discrete Helly theorems-where the common point should belong to an a-priori given set, lexicographic Helly theorems-where the common point should not be lexicographically greater than a given point, and lexicographic-discrete Helly theorems. We study the relations between the different types of the Helly theorems. We obtain several new discrete and lexicographic Helly numbers.

Original languageEnglish
Pages (from-to)690-719
Number of pages30
JournalDiscrete and Computational Geometry
Issue number4
StatePublished - Jun 2008
Externally publishedYes


  • Discrete geometry
  • Helly theorems


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