• Citer

A note on an induced subgraph characterization of domination perfect graphs

par Camby, Eglantine ;Plein, Fränk
Référence Discrete applied mathematics, 217, 3, page (711–717)
Publication Publié, 2017

Article révisé par les pairs

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

Let γ(G) and ι(G) be the domination and independent domina- tion numbers of a graph G, respectively. Introduced by Sumner and Moorer [23], a graph G is domination perfect if γ(H) = ι(H) for every induced subgraph H ⊆ G. In 1991, Zverovich and Zverovich [26] proposed a characterization of domination perfect graphs in terms of forbidden in- duced subgraphs. Fulman [15] noticed that this characterization is not correct. Later, Zverovich and Zverovich [27] offered such a second charac- terization 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 forbid- den 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