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
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).
|Additional Information:||© 2000 Springer|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
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