On Hedetniemi's conjecture and the colour template scheme
type: Item
instance of: scholarly article
title: On Hedetniemi's conjecture and the colour template scheme
zbMATH Open document ID: 1002.05028
DOI: 10.1016/S0012-365X(01)00450-2
author: Claude Tardif
author: Xuding Zhu
published in: Discrete Mathematics
publication date: 2002-08-29T00:00:00Z
review text: Hedetniemi's conjecture states that the chromatic number of a product of graphs is the minimum of the chromatic numbers of the factors. It is shown that if \(G\) and \(H\) are connected graphs of chromatic number at least 5 and both contain odd wheels as subgraphs, then their product also has chromatic number at least 5. The paper also provides counterexamples to the conjecture of El-Zahar and Saucer on the structure of \(n\)-chromatic subgraphs of products of \(n\)-chromatic graphs, implying that their method is not sufficient to prove all cases of Hedetniemi's conjecture for chromatic number larger than 4.
reviewed by: Wai-Kai Chen
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 1792443
zbMATH Keywords: homomorphism
zbMATH Keywords: chromatic number of a product of graphs
MaRDI profile type: Publication
Wikidata QID: Q122956484
description: scientific article; zbMATH DE number 1792443