Swanepoel, Konrad
(2008)
*A new proof of Vázsonyi's conjecture.*
Journal of Combinatorial Theory, Series A, 115
(5).
pp. 888-892.
ISSN 0097-3165

## 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].

Item Type: | Article |
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Official URL: | http://www.elsevier.com/wps/find/journaldescriptio... |

Additional Information: | © 2008 Elsevier |

Library of Congress subject classification: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Date Deposited: | 09 Oct 2009 09:36 |

URL: | http://eprints.lse.ac.uk/25416/ |

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