Graphs whose circular chromatic number equals the chromatic number
type: Item
instance of: scholarly article
title: Graphs whose circular chromatic number equals the chromatic number
zbMATH Open document ID: 0929.05025
author: Xuding Zhu
published in: Combinatorica
publication date: 1999-12-08T00:00:00Z
review text: The circular chromatic number of a graph is the infimum (in fact, the minimum) of \({k}/{d}\) where there is a coloring \(f\) of the vertices with colors \(1,2,\dots,k\) in such a way that \(d\leq | f(x)-f(y)| \leq k-d\) holds when \(x\), \(y\) are adjacent. Based on the notion of \(n\)-circular superedge, construtions are given for graphs with the chromatic number being equal to the circular chromatic number in the style of Hajós' method for constructing all \(n\)-chromatic graphs. This way, several new planar graphs are constructed, thus settling some earlier problems.
reviewed by: Péter Komjáth
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 1376201
zbMATH Keywords: chromatic number of graphs
MaRDI profile type: Publication
full work available at URL: s004930050050
OpenAlex ID: W2072295012
DOI: 10.1007/S004930050050
description: scientific article; zbMATH DE number 1376201