English

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.

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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}
}

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4 pages