Geodesic
Dominating bipartite subgraphs in graphs
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 1-2, pp. 85-94

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A graph G is hereditarily dominated by a class of connected graphs if each connected induced subgraph of G contains a dominating induced subgraph belonging to . In this paper we characterize graphs hereditarily dominated by classes of complete bipartite graphs, stars, connected bipartite graphs, and complete k-partite graphs.
Keywords: dominating set, dominating subgraph, forbidden induced subgraph, bipartite graph, k-partite graph 
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Bacsó, Gábor; Michalak, Danuta; Tuza, Zsolt. Dominating bipartite subgraphs in graphs. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 1-2, pp. 85-94. http://geodesic.mathdoc.fr/item/DMGT_2005_25_1-2_a9/