## Abstract

Karasev [16] 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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## Additional information

This project was done as part of the 2021 New York Discrete Math REU, funded by NSF grant DMS 2051026.

Carvalho's research was supported by the KINSC Summer Scholar program by Haverford College.

Soberón's research is supported by NSF grant DMS 2054419 and a PSC-CUNY TRADB52 award.

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CARVALHO, J.P., SOBERÓN, P. COUNTEREXAMPLES TO THE COLORFUL TVERBERG CONJECTURE FOR HYPERPLANES.
*Acta Math. Hungar.* **167**, 385–392 (2022). https://doi.org/10.1007/s10474-022-01249-8

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DOI: https://doi.org/10.1007/s10474-022-01249-8

### Key words and phrases

- Tverberg's theorem
- hyperplane arrangement
- combinatorial geometry

### Mathematics Subject Classification

- 52A37
- 52C35