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

## TL;DR

This paper determines the independence number of a Kneser graph on plane-solid flags in projective space PG(6,q) for large q, describing large maximal independent sets and bounding smaller ones.

## Contribution

It precisely characterizes all large maximal independent sets in the Kneser graph on plane-solid flags in PG(6,q) for q > 27.

## Key findings

- All maximal independent sets of size at least q^{11} are described.
- Other maximal independent sets have size at most a constant times q^{10}.
- The independence number is determined for q > 27.

## 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 $q^{10}$.