A counterexample to a conjecture on the chromatic number of r-stable Kneser hypergraphs
Abstract
The main purpose of this note is to give a counterexample to the following conjecture, raised by Florian Frick [\textit{Int. Math. Res. Not. IMRN 2020 (13), 4037-4061 (2020)}]. Conjecture. Let $r\geq 3$ and let $\mathcal{F}$ be a set system. Then $$\chi\left(\textrm{KG}^r\left(\mathcal{F}_{r-stab}\right)\right)\geq\left\lceil\frac{cd_r\left(\mathcal{F}\right)}{r-1}\right\rceil.$$
- Publication:
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arXiv e-prints
- Pub Date:
- March 2022
- DOI:
- 10.48550/arXiv.2203.03019
- arXiv:
- arXiv:2203.03019
- Bibcode:
- 2022arXiv220303019D
- Keywords:
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- Mathematics - Combinatorics