Maximal co-cliques in the Kneser graph on plane-solid flags in $PG(6,q)$

Abstract

For $q>27$ we determine the independence number $\alpha (\Gamma )$ of the Kneser graph $\Gamma$ on plane-solid flags in $PG(6,q)$. 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 $q^{10}$.