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Journal Articles Discrete and Computational Geometry Year : 2010

Carathéodory, Helly and the others in the max-plus world

Abstract

Carathéodory's, Helly's and Radon's theorems are three basic results in discrete geometry. Their max-plus or tropical analogues have been proved by various authors. We show that more advanced results in discrete geometry also have max-plus analogues, namely, the colorful Carathéodory theorem and the Tverberg theorem. A conjecture connected to the Tverberg theorem-Sierksma's conjecture-although still open for the usual convexity, is shown to be true in the max-plus setting. © 2009 Springer Science+Business Media, LLC.

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Sociology

Dates and versions

hal-00835233 , version 1 (18-06-2013)

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S. Gaubert, Frédéric Meunier. Carathéodory, Helly and the others in the max-plus world. Discrete and Computational Geometry, 2010, 43 (3), pp.648-662. ⟨10.1007/s00454-009-9207-x⟩. ⟨hal-00835233⟩
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