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Graph domination in distance two

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Bacsó G., Tálos A., Tuza Z.

Discussiones Mathematicae Graph Theory

2005

tom 25

nr 1-2

121-128

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 𝓓 of graphs, Domₖ 𝓓 is the set of those graphs G in which every connected induced subgraph H has some k-dominating induced subgraph D ∈ 𝓓 which is also connected. In our notation, Dom𝓓 coincides with Dom₁𝓓. In this paper we prove that $Dom Dom 𝓓_u = Dom₂ 𝓓_u$ holds for $𝓓_u$ = {all connected graphs without induced $P_u$} (u ≥ 2). (In particular, 𝓓₂ = {K₁} and 𝓓₃ = {all complete graphs}.) Some negative examples are also given.

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1 Discussiones Mathematicae Graph Theory

1 Bacsó G.

1 Tuza Z.

1 Tálos A.

1 2005

Wyniki wyszukiwania

Graph domination in distance two