A hilton-milner theorem for vector spaces

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

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


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 f]Fe:FF = 0 has size at most [nkz11] - qk(k~1) nkk11] + qk. 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 (US)
Pages (from-to)1-12
Number of pages12
JournalElectronic Journal of Combinatorics
Issue number1
StatePublished - 2010
Externally publishedYes


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