Convex sets in the plane with three of every four meeting

Daniel J. Kleitman, A. Gyárfás, Géza Tóth

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

Suppose we have a finite collection of closed convex sets in the plane, (which without loss of generality we can take to be polygons). Suppose further that among any four of them, some three have non-empty intersection. We show that 13 points are sufficient to meet every one of the convex sets.

Original languageEnglish
Pages (from-to)221-232
Number of pages12
JournalCombinatorica
Volume21
Issue number2
DOIs
Publication statusPublished - 2001

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Convex Sets
Closed set
Polygon
Intersection
Sufficient

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics

Cite this

Convex sets in the plane with three of every four meeting. / Kleitman, Daniel J.; Gyárfás, A.; Tóth, Géza.

In: Combinatorica, Vol. 21, No. 2, 2001, p. 221-232.

Research output: Contribution to journalArticle

Kleitman, Daniel J. ; Gyárfás, A. ; Tóth, Géza. / Convex sets in the plane with three of every four meeting. In: Combinatorica. 2001 ; Vol. 21, No. 2. pp. 221-232.
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