ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2019: 0.755

SCImago Journal Rank (SJR) 2019: 0.600

Rejection Rate (2018-2019): c. 84%

Discussiones Mathematicae Graph Theory


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


Gábor Bacsó

Computer and Automation Institute
Hungarian Academy of Sciences
H-1111 Budapest, Kende u. 13-17, Hungary

Danuta Michalak

Faculty of Mathematics
Computer Science and Econometrics
University of Zielona Góra
Podgórna 50, 65-246 Zielona Góra, Poland
Zsolt Tuza

Computer and Automation Institute
Hungarian Academy of Sciences
Department of Computer Science
University of Veszprém


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.


[1] G. Bacsó and Zs. Tuza, Dominating cliques in P5-free graphs, Periodica Math. Hungar. 21 (1990) 303-308, doi: 10.1007/BF02352694.
[2] G. Bacsó and Zs. Tuza, Domination properties and induced subgraphs, Discrete Math. 111 (1993) 37-40, doi: 10.1016/0012-365X(93)90138-J.
[3] G. Bacsó and Zs. Tuza, Structural domination in graphs, Ars Combin. 63 (2002) 235-256.
[4] G. Bacsó, Zs. Tuza and M. Voigt, Characterization of graphs dominated by paths of bounded length, to appear.
[5] M.B. Cozzens and L.L. Kelleher, Dominating cliques in graphs, in: Topics on Domination (R. Laskar and S. Hedetniemi, eds.), Discrete Math. 86 (1990) 101-116.
[6] J. Liu and H. Zhou, Dominating subgraphs in graphs with some forbidden structures, Discrete Math. 135 (1994) 163-168, doi: 10.1016/0012-365X(93)E0111-G.
[7] E.S. Wolk, The comparability graph of a tree, Proc. Amer. Math. Soc. 3 (1962) 789-795, doi: 10.1090/S0002-9939-1962-0172273-0.

Received 31 October 2003
Revised 16 June 2004