On the correspondence between tree representations of chordal and dually chordal graphs

Chordal graphs and their clique graphs (called dually chordal graphs) possess characteristic tree representations, namely, the clique tree and the compatible tree, respectively. The following problem is studied: given a chordal graph G, determine if the clique trees of G are exactly the compatible t...

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Detalles Bibliográficos
Autores: de Caria, Pablo Jesús, Gutierrez, Marisa
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2014
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/31143
Acceso en línea:http://hdl.handle.net/11336/31143
Access Level:acceso abierto
Palabra clave:Chordal Graph
Dually Chordal Graph
Basic Chordal Graph
Clique Tree
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:Chordal graphs and their clique graphs (called dually chordal graphs) possess characteristic tree representations, namely, the clique tree and the compatible tree, respectively. The following problem is studied: given a chordal graph G, determine if the clique trees of G are exactly the compatible trees of the clique graph of G. This leads to a new subclass of chordal graphs, basic chordal graphs, which is here characterized. The question is also approached backwards: given a dually chordal graph G, we find all the basic chordal graphs with clique graph equal to G. This approach leads to the possibility of considering several properties of clique trees of chordal graphs and finding their counterparts in compatible trees of dually chordal graphs.