A new proof of Vazsonyi's conjecture
Combinatorics
2008-05-13 v1 Metric Geometry
Abstract
We present a self-contained proof that the number of diameter pairs among n points in Euclidean 3-space is at most 2n-2. The proof avoids the ball polytopes used in the original proofs by Grunbaum, Heppes and Straszewicz. As a corollary we obtain that any three-dimensional diameter graph can be embedded in the projective plane.
Keywords
Cite
@article{arxiv.0705.0606,
title = {A new proof of Vazsonyi's conjecture},
author = {Konrad J Swanepoel},
journal= {arXiv preprint arXiv:0705.0606},
year = {2008}
}
Comments
4 pages