The Erdo¨s-Ko-Rado theorem for vector spaces
Journal of Combinatorial Theory Series A
On finite simple groups and Kneser graphs
Journal of Algebraic Combinatorics: An International Journal
The energy of q-Kneser graphs and attenuated q-Kneser graphs
Discrete Applied Mathematics
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Let V be a vector space of dimension v over a field of order q. The q-Kneser graph has the k-dimensional subspaces of V as its vertices, where two subspaces α and β are adjacent if and only if α ∩ β is the zero subspace. This paper is motivated by the problem of determining the chromatic numbers of these graphs. This problem is trivial when k = 1 (and the graphs are complete) or when v k (and the graphs are empty). We establish some basic theory in the general case. Then specializing to the case k = 2, we show that the chromatic number is q2 + q when v = 4 and (qV-1 - 1)/(q - 1) when v 4. In both cases we characterise the minimal colourings.