The chromatic number of the Kneser graph on chambers of a projective plane equals the incidence-free number of its incidence graph, via an elementary matching argument in symmetric designs.
A short proof of the Hilton–Milner Theorem
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A note on the chromatic number of Kneser graphs on chambers of projective planes and incidence-free sets
The chromatic number of the Kneser graph on chambers of a projective plane equals the incidence-free number of its incidence graph, via an elementary matching argument in symmetric designs.