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Helly-type theorems for polygonal curves

Swanepoel, Konrad (2002) Helly-type theorems for polygonal curves. Discrete Mathematics, 254 (1-3). pp. 527-537. ISSN 0012-365X

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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
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 09 Oct 2009 09:37
URL: http://eprints.lse.ac.uk/25414/

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