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

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:	11 Sep 2025 07:24
URI:	http://eprints.lse.ac.uk/id/eprint/25416

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