ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 24(3) (2004) 503-507
DOI: 10.7151/dmgt.1248


Gabor Bacsó and Zsolt Tuza

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


Zverovich [Discuss. Math. Graph Theory 23 (2003), 159-162.] has proved that the domination number and connected domination number are equal on all connected graphs without induced P5 and C5. Here we show (with an independent proof) that the following stronger result is also valid: Every P5-free and C5-free connected graph contains a minimum-size dominating set that induces a complete subgraph.

Keywords: graph domination, connected domination, complete subgraph, forbidden induced subgraph, characterization.

2000 Mathematics Subject Classification: 05C69.


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Received 21 July 2003
Revised 5 February 2004