Partitioning a graph into a dominating set, a total dominating set, and something else
Michael A. Henning ; Christian Löwenstein ; Dieter Rautenbach
Discussiones Mathematicae Graph Theory, Tome 30 (2010), p. 563-574 / Harvested from The Polish Digital Mathematics Library
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A recent result of Henning and Southey (A note on graphs with disjoint dominating and total dominating set, Ars Comb. 89 (2008), 159-162) implies that every connected graph of minimum degree at least three has a dominating set D and a total dominating set T which are disjoint. We show that the Petersen graph is the only such graph for which D∪T necessarily contains all vertices of the graph.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:270935 
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Michael A. Henning; Christian Löwenstein; Dieter Rautenbach. Partitioning a graph into a dominating set, a total dominating set, and something else. Discussiones Mathematicae Graph Theory, Tome 30 (2010) pp. 563-574. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1514/

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