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Colouring lines in projective space

Chowdhury, Ameera and Godsil, Chris and Royle, Gordon (2006) Colouring lines in projective space. Journal of Combinatorial Theory. Series A, 113 (1). pp. 39-52. ISSN 0097-3165. https://resolver.caltech.edu/CaltechAUTHORS:20170408-204250029

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Abstract

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 α and β are adjacent if and only if α ∩ β 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 colourings.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.jcta.2005.01.010DOIArticle
https://arxiv.org/abs/math/0507319arXivDiscussion Paper
Additional Information:© 2005 Elsevier. Received 29 September 2004, Available online 31 March 2005. The work in this paper has benefited from a number of discussions with Ada Chan.
Subject Keywords:Kneser graph; Chromatic number; Projective space
Issue or Number:1
Record Number:CaltechAUTHORS:20170408-204250029
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170408-204250029
Official Citation:Ameera Chowdhury, Chris Godsil, Gordon Royle, Colouring lines in projective space, Journal of Combinatorial Theory, Series A, Volume 113, Issue 1, 2006, Pages 39-52, ISSN 0097-3165, https://doi.org/10.1016/j.jcta.2005.01.010. (http://www.sciencedirect.com/science/article/pii/S0097316505000336)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76391
Collection:CaltechAUTHORS
Deposited By: 1Science Import
Deposited On:30 Mar 2018 23:22
Last Modified:03 Oct 2019 17:00

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