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 $q^{10}$.

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