Discussiones Mathematicae Graph Theory 25(1-2) (2005) 85-94
doi: 10.7151/dmgt.1263

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DOMINATING BIPARTITE SUBGRAPHS IN GRAPHS

Gábor Bacsó

Computer and Automation Institute
Hungarian Academy of Sciences
H-1111 Budapest, Kende u. 13-17, Hungary
e-mail: bacso@sztaki.hu

Danuta Michalak

Faculty of Mathematics
Computer Science and Econometrics
University of Zielona Góra
Podgórna 50, 65-246 Zielona Góra, Poland
e-mail: d.michalak@wmie.uz.zgora.pl
Zsolt Tuza

Computer and Automation Institute
Hungarian Academy of Sciences
and
Department of Computer Science
University of Veszprém
e-mail: tuza@lutra.sztaki.hu

Abstract

A graph G is hereditarily dominated by a class D of connected graphs if each connected induced subgraph of G contains a dominating induced subgraph belonging to D. 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.

2000 Mathematics Subject Classification: 05C69, 05C38, 05C75.

References

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Received 31 October 2003
Revised 16 June 2004