Robust Tverberg and colorful Carath\'eodory results via random choice

Research paper by Pablo Soberón

Indexed on: 20 Jul '16Published on: 20 Jul '16Published in: Mathematics - Metric Geometry


We use the probabilistic method to obtain versions of the colorful Carath\'eodory theorem and Tverberg's theorem that allow for arbitrary small sets of points to be removed without breaking the conclusion of the result. This improves the known bounds for Tverberg's theorem with tolerance and its colorful version.