Total domination in complements of graphs containing no \(K _{4,4}\)
type: Item
instance of: scholarly article
title: Total domination in complements of graphs containing no \(K _{4,4}\)
zbMATH Open document ID: 1004.05045
DOI: 10.1016/S0012-365X(01)00369-7
author: Gary MacGillivray
author: Devon McCrea
author: S. L. Fitzpatrick
published in: Discrete Mathematics
publication date: 2002-08-29T00:00:00Z
review text: For a graph \(G= (V,E)\), a set \(S\) is called a total dominating set if, for every \(v\in V\), \(N(v)\cap S\neq\varnothing\). The total domination number is the cardinality of a minimum total dominating set. The authors prove that the total domination number of a graph \(G\) whose complement \(\overline G\) does not contain \(K_{3,3}\) is at most the chromatic number of \(\overline G\) except for complete graphs and graphs belonging to a certain family, which is characterized.
reviewed by: G. Gutin
Mathematics Subject Classification ID: 05C69
zbMATH DE Number: 1792455
zbMATH Keywords: dominating sets
zbMATH Keywords: total domination
zbMATH Keywords: chromatic number
MaRDI profile type: Publication
full work available at URL: s0012-365x(01)00369-7
OpenAlex ID: W2009261722
description: scientific article; zbMATH DE number 1792455