| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4656200 | Journal of Combinatorial Theory, Series A | 2008 | 5 Pages |
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].
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
