Circular chromatic numbers of distance graphs with distance sets missing multiples
type: Item
instance of: scholarly article
title: Circular chromatic numbers of distance graphs with distance sets missing multiples
zbMATH Open document ID: 0939.05035
published in: European Journal of Combinatorics
publication date: 2000-06-29T00:00:00Z
review text: Given positive integers \(m\), \(k\), \(s\) with \(m>sk\), let \(D_{m,k,s}\) represent the set \[ \{ 1,2,\ldots ,m\}\backslash \{ k,2k,\ldots ,sk\}. \] The distance graph \(G(Z,D_{m,k,s})\) has as vertex set all integers \(Z\) and edges connecting \(i\) and \(j\) whenever \(|i-j|\in D_{m,k,s}\). This paper investigates chromatic numbers and circular chromatic numbers of the distance graphs \(G(Z,D_{m,k,s})\). By establishing bounds for the circular chromatic number \(\chi _{c}(G(Z,D_{m,k,s}))\) of \(G(Z,D_{m,k,s})\), the values of \(\chi (G(Z,D_{m,k,s}))\) are determined for all positive integers \(m\), \(k\), \(s\) and the values of \(\chi _{c}(G(Z,D_{m,k,s}))\) for some positive integers \(m\), \(k\), \(s\).
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05C12
zbMATH DE Number: 1423291
zbMATH Keywords: chromatic number
zbMATH Keywords: circular chromatic number
zbMATH Keywords: distance graph
author: Lingling Huang
author: Gerard Jennhwa Chang
reviewed by: Ioan Tomescu
MaRDI profile type: Publication
OpenAlex ID: W1996932435
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DOI: 10.1006/EUJC.1999.0284
description: scientific article; zbMATH DE number 1423291