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Gaps in convex disc packings with an application to 1-Steiner minimum trees

Swanepoel, Konrad (2000) Gaps in convex disc packings with an application to 1-Steiner minimum trees. Monatshefte fur Mathematik, 129 (3). pp. 217-226. ISSN 0026-9255

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Abstract

We show that if six translates of a convex disc C all touch C, and no two of the translates have interior points in common, then there are never more than two gaps, i.e., consecutive non-touching pairs of translates. We also characterize the configurations where there are two, one or no gaps. This result is then applied to show that the Steiner point in a 1-Steiner Minimum Tree in a normed plane has degree at most five if the unit ball is not an affine regular hexagon (where Steiner points of degree six exist).

Item Type: Article
Official URL: http://www.springerlink.com/content/103082/
Additional Information: © 2000 Springer
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: 16 Oct 2009 09:39
URL: http://eprints.lse.ac.uk/25459/

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