A new proof of Vazsonyi's conjecture

Details A new proof of Vazsonyi's conjecture A new proof of Vazsonyi's conjecture

2007-05-04

arxiv.org/abs/0705.0606v1

Journal of Combinatorial Theory, Ser. A 115 (2008) 888-892.

Mathematics

Combinatorics

4 pages

Scientific paper

10.1016/j.jcta.2007.08.006

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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