Swanepoel, Konrad (2008) A new proof of Vázsonyi's conjecture. Journal of Combinatorial Theory, Series A, 115 (5). pp. 888-892. ISSN 0097-3165
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].
|Additional Information:||© 2008 Elsevier|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
|Date Deposited:||09 Oct 2009 09:36|
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