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
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 |
| Date Deposited: | 16 Oct 2009 09:39 |
| URL: | http://eprints.lse.ac.uk/25459/ |
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