Swanepoel, Konrad 
ORCID: 0000-0002-1668-887X
(2008)
A new proof of Vázsonyi's conjecture.
Journal of Combinatorial Theory, Series A, 115 (5).
pp. 888-892.
ISSN 0097-3165
Identification Number: 10.1016/j.jcta.2007.08.006
Abstract
The diameter graph G of n points in Euclidean 3-space has a bipartite, centrally symmetric double covering on the sphere. Three easy corollaries follow: (1) A self-contained proof of Vázsonyi's conjecture that G has at most 2n−2 edges, which avoids the ball polytopes used in the original proofs given by Grünbaum, Heppes and Straszewicz. (2) G can be embedded in the projective plane. (3) Any two odd cycles in G intersect [V.L. Dol'nikov, Some properties of graphs of diameters, Discrete Comput. Geom. 24 (2000) 293–299].
| Item Type: | Article |
|---|---|
| Official URL: | http://www.elsevier.com/wps/find/journaldescriptio... |
| Additional Information: | © 2008 Elsevier |
| Divisions: | Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 09 Oct 2009 09:36 |
| Last Modified: | 13 Sep 2024 22:26 |
| URI: | http://eprints.lse.ac.uk/id/eprint/25416 |
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