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An induced subgraph characterization of domination perfect graphs

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

Authors

Igor E. Zvervich

Vadim E. Zverovich

Igor Zverovich



Abstract

Let γ(G) ι(G) be the domination number and independent domination number of a graph (G), respectively. A graph (G) is called domination perfect if γ(H) = ι(H), for every induced subgraph H of (G). There are many results giving a partial characterization of domination perfect graphs. In this paper, we present a finite induced subgraph characterization of the entire class of domination perfect graphs. The list of forbidden subgraphs in the charcterization consists of 17 minimal domination imperfect graphs. Moreover, the dominating set and independent dominating set problems are shown to be both NP‐complete on some classes of graphs. © 1995 John Wiley & Sons, Inc. Copyright © 1995 Wiley Periodicals, Inc., A Wiley Company

Citation

Zverovich, V. E., Zvervich, I. E., Zverovich, I., & Zverovich, V. (1995). An induced subgraph characterization of domination perfect graphs. Journal of Graph Theory, 20(3), 375-395. https://doi.org/10.1002/jgt.3190200313

Journal Article Type Article
Publication Date Jan 1, 1995
Journal Journal of Graph Theory
Print ISSN 0364-9024
Electronic ISSN 1097-0118
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 20
Issue 3
Pages 375-395
DOI https://doi.org/10.1002/jgt.3190200313
Keywords subgraphs, domination perfect graphs
Public URL https://uwe-repository.worktribe.com/output/1106488
Publisher URL http://dx.doi.org/10.1002/jgt.3190200313