Graph domination in distance two
Gábor Bacsó ; Attila Tálos ; Zsolt Tuza
Discussiones Mathematicae Graph Theory, Tome 25 (2005), p. 121-128 / Harvested from The Polish Digital Mathematics Library
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Let G = (V,E) be a graph, and k ≥ 1 an integer. A subgraph D is said to be k-dominating in G if every vertex of G-D is at distance at most k from some vertex of D. For a given class of graphs, Domₖ is the set of those graphs G in which every connected induced subgraph H has some k-dominating induced subgraph D ∈ which is also connected. In our notation, Dom coincides with Dom₁. In this paper we prove that DomDomu=Dom₂u holds for u = all connected graphs without induced Pu (u ≥ 2). (In particular, ₂ = K₁ and ₃ = all complete graphs.) Some negative examples are also given.

Publié le : 2005-01-01
EUDML-ID : urn:eudml:doc:270765 
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Gábor Bacsó; Attila Tálos; Zsolt Tuza. Graph domination in distance two. Discussiones Mathematicae Graph Theory, Tome 25 (2005) pp. 121-128. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1266/

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