On \(\alpha_{r}\gamma_{s}(k)\)-perfect graphs
type: Item
instance of: scholarly article
title: On \(\alpha_{r}\gamma_{s}(k)\)-perfect graphs
zbMATH Open document ID: 1030.05092
DOI: 10.1016/S0012-365X(02)00836-1
author: Dieter Rautenbach
author: Lutz Volkmann
published in: Discrete Mathematics
publication date: 2003-09-04T00:00:00Z
review text: For \(r\geq 1\), let \(\alpha_r\) and \(\gamma_r\) denote the \(r\)-distance-independence and \(r\)-distance-domination number, respectively. A graph \(G\) is \(\alpha_r\gamma_s(k)\)-perfect if \(\alpha_r(H)- \gamma_s(H)\leq k\) for every induced subgraph \(H\) of \(G\). In 1999, I. Zverovich characterized \(\alpha_1\gamma_1(k)\)-perfect graphs. The present authors characterize claw-free \(\alpha_2\gamma_2(k)\)-perfect graphs and \(\alpha_{2r-1}\gamma_r(k)\)-perfect graphs for \(r\geq 1\).
Mathematics Subject Classification ID: 05C69
zbMATH DE Number: 1974995
zbMATH Keywords: domination perfect graphs
zbMATH Keywords: distance domination number
zbMATH Keywords: distance independence number
reviewed by: G. Gutin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1974995