Separating convex sets by straight lines

Jaݩnos Pach, Gaݩbor Tardos

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We answer some questions of Tverberg about separability properties of families of convex sets. In particular, we show that there is a family of infinitely many pairwise disjoint closed disks, no two of which can be separated from two others by a straight line. No such construction exists with equal disks. We also prove that every uncountable family of pairwise disjoint convex sets in the plane has two uncountable subfamilies that an be separated by a straight line.

Original languageEnglish
Pages (from-to)427-433
Number of pages7
JournalDiscrete Mathematics
Volume241
Issue number1-3
DOIs
Publication statusPublished - Oct 28 2001

Keywords

  • Convex sets
  • Infinite families
  • Separation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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