English

Counterexamples to the Colorful Tverberg Conjecture for Hyperplanes

Combinatorics 2021-08-19 v2

Abstract

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

Keywords

Cite

@article{arxiv.2108.07680,
  title  = {Counterexamples to the Colorful Tverberg Conjecture for Hyperplanes},
  author = {João Pedro Carvalho and Pablo Soberón},
  journal= {arXiv preprint arXiv:2108.07680},
  year   = {2021}
}

Comments

5 pages, 1 figure

R2 v1 2026-06-24T05:11:36.517Z