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A semi-induced subgraph characterization of upper domination perfect graphs

Zverovich, Igor E.; Zverovich, Vadim E.; Zverovich, Igor; Zverovich, Vadim

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Authors

Igor E. Zverovich

Vadim E. Zverovich

Igor Zverovich



Abstract

Let β(G) and Γ(G) be the independence number and the upper domination number of a graph G, respectively. A graph G is called Γ-perfect if β(H) = Γ(H), for every induced subgraph H of G. The class of Γ-perfect graphs generalizes such well-known classes of graphs as strongly perfect graphs, absorbantly perfect graphs, and circular arc graphs. In this article, we present a characterization of Γ-perfect graphs in terms of forbidden semi-induced subgraphs. Key roles in the characterization are played by the odd prism and the even Möbius ladder, where the prism and the Möbius ladder are well-known 3-regular graphs [2]. Using the semi-induced subgraph characterization, we obtain a characterization of K 1.3-free Γ-perfect graphs in terms of forbidden induced subgraphs. © 1999 John Wiley & Sons, Inc.

Citation

Zverovich, V. E., Zverovich, I. E., Zverovich, I., & Zverovich, V. (1999). A semi-induced subgraph characterization of upper domination perfect graphs. Journal of Graph Theory, 31(1), 29-49. https://doi.org/10.1002/%28SICI%291097-0118%28199905%2931%3A1%3C29%3A%3AAID-JGT4%3E3.0.CO%3B2-G

Journal Article Type Article
Publication Date Jan 1, 1999
Deposit Date Sep 24, 2015
Publicly Available Date Feb 9, 2016
Journal Journal of Graph Theory
Print ISSN 0364-9024
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 31
Issue 1
Pages 29-49
DOI https://doi.org/10.1002/%28SICI%291097-0118%28199905%2931%3A1%3C29%3A%3AAID-JGT4%3E3.0.CO%3B2-G
Keywords upper domination perfect graphs, semi-induced subgraph characterization
Public URL https://uwe-repository.worktribe.com/output/1096875
Publisher URL http://dx.doi.org/10.1002/(SICI)1097-0118(199905)31:13.0.CO;2-G
Additional Information Additional Information : This is the peer reviewed version of the following article: Zverovich, I. and Zverovich, V. (1999) A semi-induced subgraph characterization of upper domination perfect graphs. Journal of Graph Theory, 31 (1). pp. 29-49. ISSN 0364-9024, which has been published in final form at http://dx.doi.org/10.1002/(SICI)1097-0118(199905)31:13.0.CO;2-G. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.

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