10.1016/S0012-365X(03)00187-0Discrete Mathematics272197-105DSMH

Bock Boom Lim

Clark

Colbourn

Cozzens

Garey

Haynes

Joseph

Khee Meng Koh

Peter J. Slater

Proskurowski

Sampathkumar

AbstractLet H be some fixed graph of order p. For a given graph G and vertex set S⊆V(G), we say that S is H-decomposable if S can be partitioned as S=S1∪S2∪⋯∪Sj where, for each of the disjoint subsets Si, with 1⩽i⩽j, we have |Si|=p and H is a spanning subgraph of 〈Si〉, the subgraph induced by Si. We define the H-domination number of G, denoted as γH(G), to be the minimum cardinality of an H-decomposable dominating set S. If no such dominating set exists, we write γH(G)=∞. We show that the associated H-domination decision problem is NP-complete for every choice of H. Bounds are shown for γH(G). We show, in particular, that if δ(G)⩾2, then γP3(G)⩽3γ(G). Also, if γP3(G)=3γ(G), then every γ(G)-set is an efficient dominating set

Koh, Khee Meng

Lim, Bock Boom

Slater, Peter J.

Elsevier - Publisher Connector 

H-domination in graphs 

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H-domination in graphs

Koh, K.M.

Lim, B.B.

Slater, P.J.

ScholarBank@NUS

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H-domination in graphs

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Elsevier - Publisher Connector

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