A Hilton-Milner theorem for vector spaces

A. Blokhuis, A.E. Brouwer, A. Chowdhury, P. Frankl, T.J.J. Mussche, B. Patkós, T. Szönyi

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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.
Original languageEnglish
Pages (from-to)R71-1/12
JournalThe Electronic Journal of Combinatorics
Issue number1
Publication statusPublished - 2010


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