@article{2438,
abstract = {The colored Tverberg theorem asserts that for eve;ry d and r there exists t=t(d,r) such that for every set C ⊂ ℝ d of cardinality (d + 1)t, partitioned into t-point subsets C 1, C 2,...,C d+1 (which we think of as color classes; e. g., the points of C 1 are red, the points of C 2 blue, etc.), there exist r disjoint sets R 1, R 2,...,R r⊆C that are rainbow, meaning that {pipe}R i∩C j{pipe}≤1 for every i,j, and whose convex hulls all have a common point. All known proofs of this theorem are topological. We present a geometric version of a recent beautiful proof by Blagojević, Matschke, and Ziegler, avoiding a direct use of topological methods. The purpose of this de-topologization is to make the proof more concrete and intuitive, and accessible to a wider audience.},
author = {Matoušek, Jiří and Martin Tancer and Uli Wagner},
journal = {Discrete & Computational Geometry},
number = {2},
pages = {245 -- 265},
publisher = {Springer},
title = {{A geometric proof of the colored Tverberg theorem}},
doi = {10.1007/s00454-011-9368-2},
volume = {47},
year = {2012},
}