  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.

Combinatorics