Colouring lines in projective space

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:113

Article

Chowdhury, A ; Godsil, C ; Royle, G

关键词: Kneser graph;    chromatic number;    projective space;   

DOI  :  10.1016/j.jcta.2005.01.010

来源: Elsevier

【 摘 要 】

Let V be a vector space of dimension v over a field of order q. The q-Kneser graph has the k-dimensional subspaces of V as its vertices, where two subspaces alpha and beta are adjacent if and only if alpha boolean AND beta is the zero subspace. This paper is motivated by the problem of determining the chromatic numbers oF these graphs. This problem is trivial when k = 1 (and the graphs are complete) or when v < 2k (and the graphs are empty). We establish some basic theory in the general case. Then specializing to the case k = 2, we show that the chromatic number is q(2) + q when v = 4 and (q(v-1) - 1)/(q - 1) when v > 4. In both cases we characterise the minimal colourrings. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free