\(\iota(G)\) be the domination and independent domination numbers of a graph
\(G\), respectively. Introduced by Sumner and Moorer (1979), a graph
\(G\) is domination perfect if
\(\gamma(H) = \iota(H)\) for every induced subgraph
\(H \subseteq G\).
In 1991, Zverovich and Zverovich (1991)proposed a characterization of domination perfect graphs in terms of forbidden induced subgraphs. Fulman (1993) noticed that this characterization is not correct.
Later, Zverovich and Zverovich (1995) offered such a second characterization with 17 forbidden induced subgraphs. However, the latter still needs to be adjusted.
In this paper, we point out a counterexample. We then give a new characterization of domination perfect graphs in terms of only 8 forbidden induced subgraphs and a short proof thereof.
Moreover, in the class of domination perfect graphs, we propose a polynomial-time algorithm computing, given a dominating set
\(D\), an independent dominating set
\(Y\) such that
\(|Y| \leq |D|\).
Published April 2016 , 12 pages