On \(b\)-coloring of the Kneser graphs
type: Item
instance of: scholarly article
title: On \(b\)-coloring of the Kneser graphs
zbMATH Open document ID: 1198.05057
author: Ramin Javadi
author: Behnaz Omoomi
published in: Discrete Mathematics
publication date: 2009-12-10T00:00:00Z
review text: Let \(G\) be a graph without loops and multiple edges. A \(b\)-colouring of \(G\) by \(k\) colours is a proper \(k\)-colouring of \(G\) such that in each colour class there is a vertex having neighbours in all the other \(k-1\) colour classes. The \(b\)-chromatic number of a graph \(G\) is the maximum number \(k\) for which \(G\) has a \(b\)-colouring by \(k\) colours. A graph \(G\) is \(b\)-continuous if for every \(k\) between the chroamtic nuumber and the \(b\)-chromatic number there is a \(b\)-colouring of \(G\) by \(k\) colours. In the present paper, \(b\)-colourings of Kneser graphs \(K(n, k)\) are studied. Moreover, it is proved that \(K(n, 2)\) is \(b\)-continuous for \(n\geq 17\).
reviewed by: Ulrike Baumann
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 5644957
zbMATH Keywords: \(b\)-chromatic number
zbMATH Keywords: \(b\)-coloring
zbMATH Keywords: dominating coloring
zbMATH Keywords: \(b\)-continuous graph
zbMATH Keywords: Kneser graph
zbMATH Keywords: Steiner triple system
MaRDI profile type: Publication
full work available at URL: j.disc.2009.01.017
OpenAlex ID: W2030051419
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cites work: Kneser's conjecture, chromatic number, and homotopy
DOI: 10.1016/J.DISC.2009.01.017
description: scientific article; zbMATH DE number 5644957