Vol. 18, No. 1, 2020
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Maximal cocliques in the Kneser graph on plane-solid flags in $\mathrm{PG}(6,q)$

Klaus Metsch and Daniel Werner
Vol. 18 (2020), No. 1, 39–55
DOI: 10.2140/iig.2020.18.39
Abstract

For q ≥ 27 we determine the independence number α(Γ) of the Kneser graph Γ on plane-solid flags in PG(6,q). More precisely we describe all maximal independent sets of size at least q11 and show that every other maximal example has cardinality at most a constant times q10.

Keywords
Kneser graph, Erdös–Ko–Rado set, independent set
Mathematical Subject Classification 2010
Primary: 05C35, 05C69, 51E20, 05B25
Milestones
Received: 24 April 2019
Revised: 5 May 2020
Accepted: 22 May 2020
Published: 21 November 2020
Authors
Klaus Metsch
Mathematisches Institut
Justus-Liebig-Universität
Arndtstraße 2
35392 Gießen
Germany
Daniel Werner
Mathematisches Institut
Justus-Liebig-Universität
Arndtstraße 2
35392 Gießen
Germany