Swanepoel, Konrad 
ORCID: 0000-0002-1668-887X
(2002)
Helly-type theorems for polygonal curves.
Discrete Mathematics, 254 (1-3).
pp. 527-537.
ISSN 0012-365X
Abstract
We prove the following intersection and covering Helly-type theorems for boundaries of convex polygons in the plane. • Let S be a set of points in the plane. Let n4. If any 2n+2 points of S can be covered by the boundary of a convex n-gon, then S can be covered by the boundary of a convex n-gon. The value of 2n+2 is best possible in general. If n=3, 2n+2 can be reduced to 7. • Let be a finite collection of boundaries of convex n-gons, n5. If any 3n−3 members of have non-empty intersection, then has non-empty intersection. The value 3n−3 is best possible in general. For n=3 and 4, the value 3n−3 can be reduced to 8 and 10, respectively.
| Item Type: | Article |
|---|---|
| Official URL: | http://www.elsevier.com/wps/find/journaldescriptio... |
| Additional Information: | © 2002 Elsevier |
| Divisions: | Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 09 Oct 2009 09:37 |
| Last Modified: | 13 Sep 2024 21:34 |
| URI: | http://eprints.lse.ac.uk/id/eprint/25414 |
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