Acyclic edge colourings of graphs with large girth

An edge colouring of a graph \(G\) is called acyclic if it is proper and every cycle contains at least three colours. We show that for every \(\varepsilon>0\), there exists a \(g=g(\varepsilon)\) such that if \(G\) has girth at least \(g\) then \(G\) admits an acyclic edge colouring with at most...

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Bibliographic Details
Published inarXiv.org
Main Authors Xing Shi Cai, Perarnau, Guillem, Reed, Bruce, Watts, Adam Bene
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 23.06.2016
Subjects
Computer Science - Discrete Mathematics
Graph coloring
Mathematics - Combinatorics
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Summary:An edge colouring of a graph \(G\) is called acyclic if it is proper and every cycle contains at least three colours. We show that for every \(\varepsilon>0\), there exists a \(g=g(\varepsilon)\) such that if \(G\) has girth at least \(g\) then \(G\) admits an acyclic edge colouring with at most \((1+\varepsilon)\Delta\) colours.
ISSN:2331-8422
DOI:10.48550/arxiv.1411.3047