A Hilton-Milner theorem for vector spaces

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

A Hilton-Milner theorem for vector spaces

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

Discrete Algebra and Geometry

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

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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.

Originele taal-2	Engels
Pagina's (van-tot)	R71-1/12
Tijdschrift	The Electronic Journal of Combinatorics
Volume	17
Nummer van het tijdschrift	1
Status	Gepubliceerd - 2010

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title = "A Hilton-Milner theorem for vector spaces",

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 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.",

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T1 - A Hilton-Milner theorem for vector spaces

AU - Blokhuis, A.

AU - Brouwer, A.E.

AU - Chowdhury, A.

AU - Frankl, P.

AU - Mussche, T.J.J.

AU - Patkós, B.

AU - Szönyi, 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 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.

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 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.

M3 - Article

SN - 1077-8926

VL - 17

SP - R71-1/12

JO - The Electronic Journal of Combinatorics

JF - The Electronic Journal of Combinatorics

IS - 1

ER -

A Hilton-Milner theorem for vector spaces

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