A counterexample to a conjecture on the chromatic number of r-stable Kneser hypergraphs

Hamid Reza Daneshpajouh

A counterexample to a conjecture on the chromatic number of r-stable Kneser hypergraphs

Combinatorics 2022-03-21 v2

Authors: Hamid Reza Daneshpajouh

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 $\chi\left(\textrm{KG}^r\left(\mathcal{F}_{r-stab}\right)\right)\geq\left\lceil\frac{cd_r\left(\mathcal{F}\right)}{r-1}\right\rceil.$

Keywords

chromatic number kneser hypergraphs r-stable counterexample set system conjecture

Cite

@article{arxiv.2203.03019,
  title  = {A counterexample to a conjecture on the chromatic number of r-stable Kneser hypergraphs},
  author = {Hamid Reza Daneshpajouh},
  journal= {arXiv preprint arXiv:2203.03019},
  year   = {2022}
}

A counterexample to a conjecture on the chromatic number of r-stable Kneser hypergraphs

Abstract

Keywords

Cite

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