An induced subgraph characterization of domination perfect graphs

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

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

• 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