{k}-domination for chordal graphs and related graph classes
In this work we obtain a new graph class where the {. k}-dominating function problem ({. k}-DOM) is NP-complete: the class of chordal graphs. We also identify some maximal subclasses for which it is polynomial time solvable. Firstly, by relating this problem with the k-dominating function problem (k...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2013 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositório: | CONICET Digital (CONICET) |
| Idioma: | inglês |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/94349 |
| Acesso em linha: | http://hdl.handle.net/11336/94349 |
| Access Level: | Acceso aberto |
| Palavra-chave: | CHORDAL GRAPH COMPUTATIONAL COMPLEXITY K-DOMINATING FUNCTION {K}-DOMINATING FUNCTION https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | In this work we obtain a new graph class where the {. k}-dominating function problem ({. k}-DOM) is NP-complete: the class of chordal graphs. We also identify some maximal subclasses for which it is polynomial time solvable. Firstly, by relating this problem with the k-dominating function problem (k-DOM), we prove that {. k}-DOM is polynomial time solvable for strongly chordal graphs. Besides, by expressing the property involved in k-DOM in Counting Monadic Second-order Logic, we obtain that both problems are linear time solvable for bounded tree-width graphs. Finally, we show that {. k}-DOM is linear time solvable for spider graphs. |
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