#### Vol. 18, No. 1, 2020

 Recent Issues Volume 18 Volume 16 Volume 15 Volume 14 Volume 13 Volume 12 Volume 11 Volume 10 Volume 9 Volume 8 Volume 6+7 Volume 5 Volume 4 Volume 3 Volume 2 Volume 1
 The Journal About the Journal Editorial Board Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN (electronic): 2640-7345 ISSN (print): 2640-7337 Author Index To Appear Other MSP Journals
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
##### Abstract

For $q\ge 27$ we determine the independence number $\alpha \left(\Gamma \right)$ of the Kneser graph $\Gamma$ on plane-solid flags in PG$\left(6,q\right)$. More precisely we describe all maximal independent sets of size at least ${q}^{11}$ and show that every other maximal example has cardinality at most a constant times ${q}^{10}$.

##### Keywords
Kneser graph, Erdös–Ko–Rado set, independent set
##### Mathematical Subject Classification 2010
Primary: 05C35, 05C69, 51E20, 05B25