# Dominating bipartite subgraphs in graphs

Gábor Bacsó; Danuta Michalak; Zsolt Tuza

Discussiones Mathematicae Graph Theory (2005)

- Volume: 25, Issue: 1-2, page 85-94
- ISSN: 2083-5892

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topGábor Bacsó, Danuta Michalak, and Zsolt Tuza. "Dominating bipartite subgraphs in graphs." Discussiones Mathematicae Graph Theory 25.1-2 (2005): 85-94. <http://eudml.org/doc/270730>.

@article{GáborBacsó2005,

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.},

author = {Gábor Bacsó, Danuta Michalak, Zsolt Tuza},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {dominating set; dominating subgraph; forbidden induced subgraph; bipartite graph; k-partite graph; -partitie graph},

language = {eng},

number = {1-2},

pages = {85-94},

title = {Dominating bipartite subgraphs in graphs},

url = {http://eudml.org/doc/270730},

volume = {25},

year = {2005},

}

TY - JOUR

AU - Gábor Bacsó

AU - Danuta Michalak

AU - Zsolt Tuza

TI - Dominating bipartite subgraphs in graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2005

VL - 25

IS - 1-2

SP - 85

EP - 94

AB - 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.

LA - eng

KW - dominating set; dominating subgraph; forbidden induced subgraph; bipartite graph; k-partite graph; -partitie graph

UR - http://eudml.org/doc/270730

ER -

## References

top- [1] G. Bacsó and Zs. Tuza, Dominating cliques in P₅-free graphs, Periodica Math. Hungar. 21 (1990) 303-308, doi: 10.1007/BF02352694. Zbl0746.05065
- [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. Zbl1114.05069
- [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. Zbl0729.05043
- [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. Zbl0812.05052
- [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. Zbl0109.16402

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