Swanepoel, Konrad
(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 |
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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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