We show for k = 2 that if q = 3 and n = 2k + 1, or q = 2 and n = 2k + 2, then any intersecting family F of k-subspaces of an n-dimensional vector space over GF(q) with nF¿F F = 0 has size at most (formula). This bound is sharp as is shown by Hilton-Milner type families. As an application of this result, we determine the chromatic number of the corresponding q-Kneser graphs.
|Journal||The Electronic Journal of Combinatorics|
|Publication status||Published - 2010|