On the complexity of { k } -domination and k-tuple domination in graphs

We consider two types of graph domination - {k}-domination and k-tuple domination, for a fixed positive integer k - and provide new NP-complete as well as polynomial time solvable instances for their related decision problems. Regarding NP-completeness results, we solve the complexity of the {k}-dom...

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Detalles Bibliográficos
Autores: Argiroffo, Gabriela Rut, Leoni, Valeria Alejandra, Torres, Pablo Daniel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2015
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/49955
Acceso en línea:http://hdl.handle.net/11336/49955
Access Level:acceso abierto
Palabra clave:Chordal Graphs
Computational Complexity
K-Tuple Domination
Planar Graphs
Split Graphs
{ K } Domination
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:We consider two types of graph domination - {k}-domination and k-tuple domination, for a fixed positive integer k - and provide new NP-complete as well as polynomial time solvable instances for their related decision problems. Regarding NP-completeness results, we solve the complexity of the {k}-domination problem on split graphs, chordal bipartite graphs and planar graphs, left open in 2008. On the other hand, by exploiting Courcelle's results on Monadic Second Order Logic, we obtain that both problems are polynomial time solvable for graphs with clique-width bounded by a constant. In addition, we give an alternative proof for the linearity of these problems on strongly chordal graphs.