### 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:F}F = 0 has size at most [^{n}_{k}z_{1}^{1}] - q^{k(k}~^{1) n}_{k}^{k}_{1}^{1}] + 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.

Original language | English |
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Pages (from-to) | 1-12 |

Number of pages | 12 |

Journal | Electronic Journal of Combinatorics |

Volume | 17 |

Issue number | 1 |

Publication status | Published - 2010 |

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### ASJC Scopus subject areas

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

### Cite this

*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.

Research output: Contribution to journal › Article

*Electronic Journal of Combinatorics*, vol. 17, no. 1, pp. 1-12.

}

TY - JOUR

T1 - A hilton-milner theorem for vector spaces

AU - Blokhuis, A.

AU - Brouwer, A. E.

AU - Chowdhury, A.

AU - Frankl, P.

AU - Mussche, T.

AU - Patkós, B.

AU - Szőnyi, T.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77955631202&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955631202&partnerID=8YFLogxK

M3 - Article

VL - 17

SP - 1

EP - 12

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

SN - 1077-8926

IS - 1

ER -