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Perfect Partitions of Convex Sets in the Plane

✍ Scribed by Kaneko; Kano

Publisher
Springer
Year
2002
Tongue
English
Weight
133 KB
Volume
28
Category
Article
ISSN
0179-5376

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πŸ“œ SIMILAR VOLUMES

Separating convex sets in the plane
Separating convex sets in the plane
✍ Jurek Czyzowicz; Eduardo Rivera-Campo; Jorge Urrutia; Joseph Zaks πŸ“‚ Article πŸ“… 1992 πŸ› Springer 🌐 English βš– 329 KB
On Separation of Plane Convex Sets
On Separation of Plane Convex Sets
✍ Eduardo Rivera-Campo; JenΓΆ TΓΆrΓΆcsik πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 77 KB

We show that in any family \(F\) of \(n \geqslant 5\) convex sets in the plane with pairwise disjoint relative interiors, there are two sets \(A\) and \(B\) such that every line that separates them, separates either \(A\) or \(B\) from at least \((n+28) / 30\) sets in \(F\).