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Upper domination and upper irredundance perfect graphs

Gutin, Gregory; Zverovich, Vadim

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Authors

Gregory Gutin



Abstract

Let β(G), Γ(G) and IR(G) be the independence number, the upper domination number and the upper irredundance number, respectively. A graph G is called Γ-perfect if β(H) = Γ(H), for every induced subgraph H of G. A graph G is called IR-perfect if Γ(H) = IR(H), for every induced subgraph H of G. In this paper, we present a characterization of Γ-perfect graphs in terms of a family of forbidden induced subgraphs, and show that the class of Γ-perfect graphs is a subclass of IR-perfect graphs and that the class of absorbantly perfect graphs is a subclass of Γ-perfect graphs. These results imply a number of known theorems on Γ-perfect graphs and IR-perfect graphs. Moreover, we prove a sufficient condition for a graph to be Γ-perfect and IR-perfect which improves a known analogous result. © 1998 Elsevier Science B.V. All rights reserved.

Citation

Gutin, G., & Zverovich, V. (1998). Upper domination and upper irredundance perfect graphs. Discrete Mathematics, 190(1-3), 95-105. https://doi.org/10.1016/S0012-365X%2898%2900036-3

Journal Article Type Article
Publication Date Aug 28, 1998
Deposit Date Sep 24, 2015
Publicly Available Date Feb 19, 2016
Journal Discrete Mathematics
Print ISSN 0012-365X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 190
Issue 1-3
Pages 95-105
DOI https://doi.org/10.1016/S0012-365X%2898%2900036-3
Keywords independence number, upper domination number, upper irredundance number
Public URL https://uwe-repository.worktribe.com/output/1099501
Publisher URL http://dx.doi.org/10.1016/S0012-365X(98)00036-3

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