Blokhuis, A.; Brouwer, A. E.; Chowdhury, A.; Frankl, P.; Mussche, T.; Patkós, B.; Szönyi, T. A Hilton-Milner theorem for vector spaces. (English) Zbl 1189.05171 Electron. J. Comb. 17, No. 1, Research Paper R71, 12 p. (2010). Summary: We show for \(k \geq 2\) that if \(q\geq 3\) and \(n \geq 2k+1\), or \(q=2\) and \(n \geq 2k+2\), then any intersecting family \({\mathcal F}\) of \(k\)-subspaces of an \(n\)-dimensional vector space over \(GF(q)\) with \(\bigcap_{F \in {\mathcal F}} F=0\) has size at most \(\left[{n-1\atop k-1}\right]-q^{k(k-1)}\left[{n-k-1\atop k-1}\right]+q^k\). 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. Cited in 36 Documents MSC: 05D05 Extremal set theory 05A30 \(q\)-calculus and related topics PDFBibTeX XMLCite \textit{A. Blokhuis} et al., Electron. J. Comb. 17, No. 1, Research Paper R71, 12 p. (2010; Zbl 1189.05171) Full Text: EuDML EMIS