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

2022/03/06 by Hamid Reza Daneshpajouh, Daneshpajouh, Hamid Reza · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Geometry #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2203.03019

openalex publication_date 2022/03/06 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

The main purpose of this note is to give a counterexample to the following\nconjecture, raised by Florian Frick [\Int. Math. Res. Not. IMRN 2020\n(13), 4037-4061 (2020)].\n Conjecture. Let r\≥ 3 and let \F be a set system. Then\n
chi
left(
textrmKG^r
left(
mathcalF_r-stab
right)
right)
geq
left
lceil
fraccd_r
left(
mathcalF
right)r-1
right
rceil.\n

Cited by

• On the Chromatic Number of Stable Kneser Hypergraphs: Verifying the Conjecture for New Families

Related

• On the Chromatic Number of Stable Kneser Hypergraphs: Verifying the Conjecture for New Families
• The chromatic number of almost stable Kneser hypergraphs
• Chromatic numbers of stable Kneser hypergraphs via topological Tverberg-type theorems
• On the chromatic number of almost stable general Kneser hypergraphs
• On the chromatic number of generalized Kneser hypergraphs