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A new proof of Vázsonyi's conjecture

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

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Identification Number: 10.1016/j.jcta.2007.08.006


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
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Additional Information: © 2008 Elsevier
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 09 Oct 2009 09:36
Last Modified: 17 Jun 2024 19:24

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