A hilton-milner theorem for vector spaces

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

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

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
Pages (from-to)1-12
Number of pages12
JournalElectronic Journal of Combinatorics
Volume17
Issue number1
Publication statusPublished - 2010

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Kneser Graph
Intersecting Family
Vector spaces
Chromatic number
Vector space
n-dimensional
Subspace
Theorem
Family

ASJC Scopus subject areas

  • Geometry and Topology
  • Theoretical Computer Science
  • Computational Theory and Mathematics

Cite this

Blokhuis, A., Brouwer, A. E., Chowdhury, A., Frankl, P., Mussche, T., Patkós, B., & Szőnyi, T. (2010). A hilton-milner theorem for vector spaces. Electronic Journal of Combinatorics, 17(1), 1-12.

A hilton-milner theorem for vector spaces. / Blokhuis, A.; Brouwer, A. E.; Chowdhury, A.; Frankl, P.; Mussche, T.; Patkós, B.; Szőnyi, T.

In: Electronic Journal of Combinatorics, Vol. 17, No. 1, 2010, p. 1-12.

Research output: Contribution to journalArticle

Blokhuis, A, Brouwer, AE, Chowdhury, A, Frankl, P, Mussche, T, Patkós, B & Szőnyi, T 2010, 'A hilton-milner theorem for vector spaces', Electronic Journal of Combinatorics, vol. 17, no. 1, pp. 1-12.
Blokhuis A, Brouwer AE, Chowdhury A, Frankl P, Mussche T, Patkós B et al. A hilton-milner theorem for vector spaces. Electronic Journal of Combinatorics. 2010;17(1):1-12.
Blokhuis, A. ; Brouwer, A. E. ; Chowdhury, A. ; Frankl, P. ; Mussche, T. ; Patkós, B. ; Szőnyi, T. / A hilton-milner theorem for vector spaces. In: Electronic Journal of Combinatorics. 2010 ; Vol. 17, No. 1. pp. 1-12.
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