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

Swanepoel, Konrad ORCID: 0000-0002-1668-887X (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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Identification Number: 10.1007/s006050050072

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
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	16 Oct 2009 09:39
Last Modified:	11 Dec 2024 22:15
URI:	http://eprints.lse.ac.uk/id/eprint/25459

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