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arXiv · 2108.07680

Counterexamples to the Colorful Tverberg Conjecture for Hyperplanes

João Pedro Carvalho·Pablo Soberón
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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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João Pedro Carvalho, Pablo Soberón. 2021-08-18. Counterexamples to the Colorful Tverberg Conjecture for Hyperplanes. https://arxiv.org/abs/2108.07680

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