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Carathéodory, Helly and the Others in the Max-Plus World

Carathéodory, Helly and the Others in the Max-Plus World,10.1007/s00454-009-9207-x,Discrete & Computational Geometry,Stephane Gaubert,Frédéric Meunier

Carathéodory, Helly and the Others in the Max-Plus World   (Citations: 5)
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Carath\'eodory's, Helly's and Radon's theorems are three basic results in discrete geometry. Their max-plus counterparts have been proved by various authors. In this paper, more advanced results in discrete geometry are shown to have also their max-plus counterparts: namely, the colorful Carath\'eodory 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 settings.
Journal: Discrete & Computational Geometry - DCG , vol. 43, no. 3, pp. 648-662, 2010
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