Counterexamples to the Colorful Tverberg Conjecture for Hyperplanes
Abstract
In 2008 Karasev conjectured that for every set of r blue lines, r green lines, and r red lines in the plane, there exists a partition of them into r colorful triples whose induced triangles intersect. We disprove this conjecture for every r and extend the counterexamples to higher dimensions.
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