Determining what sets of trees can be the clique trees of a chordal graph
- Autores
- De Caria, Pablo Jesús; Gutiérrez, Marisa
- Año de publicación
- 2011
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Chordal graphs have characteristic tree representations, the clique trees. The problems of finding one or enumerating them have already been solved in a satisfactory way. In this paper, the following related problem is studied: given a family T of trees, all having the same vertex set V, determine whether there exists a chordal graph whose set of clique trees equals T. For that purpose, we undertake a study of the structural properties, some already known and some new, of the clique trees of a chordal graph and the characteristics of the sets that induce subtrees of every clique tree. Some necessary and sufficient conditions and examples of how they can be applied are found, eventually establishing that a positive or negative answer to the problem can be obtained in polynomial time. If affirmative, a graph whose set of clique trees equals T is also obtained. Finally, all the chordal graphs with set of clique trees equal to T are characterized.
Facultad de Ciencias Exactas - Materia
-
Matemática
Ciencias Exactas
Chordal graph
Clique
Clique tree
Minimal separator - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/97141
Ver los metadatos del registro completo
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Determining what sets of trees can be the clique trees of a chordal graphDe Caria, Pablo JesúsGutiérrez, MarisaMatemáticaCiencias ExactasChordal graphCliqueClique treeMinimal separatorChordal graphs have characteristic tree representations, the clique trees. The problems of finding one or enumerating them have already been solved in a satisfactory way. In this paper, the following related problem is studied: given a family T of trees, all having the same vertex set V, determine whether there exists a chordal graph whose set of clique trees equals T. For that purpose, we undertake a study of the structural properties, some already known and some new, of the clique trees of a chordal graph and the characteristics of the sets that induce subtrees of every clique tree. Some necessary and sufficient conditions and examples of how they can be applied are found, eventually establishing that a positive or negative answer to the problem can be obtained in polynomial time. If affirmative, a graph whose set of clique trees equals T is also obtained. Finally, all the chordal graphs with set of clique trees equal to T are characterized.Facultad de Ciencias Exactas2011-11-22info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/97141enginfo:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/81353info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs13173-011-0048-0info:eu-repo/semantics/altIdentifier/issn/1678-4804info:eu-repo/semantics/altIdentifier/doi/10.1007/s13173-011-0048-0info:eu-repo/semantics/altIdentifier/hdl/11336/81353info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/2.5/ar/Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-10T12:23:06Zoai:sedici.unlp.edu.ar:10915/97141Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-10 12:23:06.337SEDICI (UNLP) - Universidad Nacional de La Platafalse |
| dc.title.none.fl_str_mv |
Determining what sets of trees can be the clique trees of a chordal graph |
| title |
Determining what sets of trees can be the clique trees of a chordal graph |
| spellingShingle |
Determining what sets of trees can be the clique trees of a chordal graph De Caria, Pablo Jesús Matemática Ciencias Exactas Chordal graph Clique Clique tree Minimal separator |
| title_short |
Determining what sets of trees can be the clique trees of a chordal graph |
| title_full |
Determining what sets of trees can be the clique trees of a chordal graph |
| title_fullStr |
Determining what sets of trees can be the clique trees of a chordal graph |
| title_full_unstemmed |
Determining what sets of trees can be the clique trees of a chordal graph |
| title_sort |
Determining what sets of trees can be the clique trees of a chordal graph |
| dc.creator.none.fl_str_mv |
De Caria, Pablo Jesús Gutiérrez, Marisa |
| author |
De Caria, Pablo Jesús |
| author_facet |
De Caria, Pablo Jesús Gutiérrez, Marisa |
| author_role |
author |
| author2 |
Gutiérrez, Marisa |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
Matemática Ciencias Exactas Chordal graph Clique Clique tree Minimal separator |
| topic |
Matemática Ciencias Exactas Chordal graph Clique Clique tree Minimal separator |
| dc.description.none.fl_txt_mv |
Chordal graphs have characteristic tree representations, the clique trees. The problems of finding one or enumerating them have already been solved in a satisfactory way. In this paper, the following related problem is studied: given a family T of trees, all having the same vertex set V, determine whether there exists a chordal graph whose set of clique trees equals T. For that purpose, we undertake a study of the structural properties, some already known and some new, of the clique trees of a chordal graph and the characteristics of the sets that induce subtrees of every clique tree. Some necessary and sufficient conditions and examples of how they can be applied are found, eventually establishing that a positive or negative answer to the problem can be obtained in polynomial time. If affirmative, a graph whose set of clique trees equals T is also obtained. Finally, all the chordal graphs with set of clique trees equal to T are characterized. Facultad de Ciencias Exactas |
| description |
Chordal graphs have characteristic tree representations, the clique trees. The problems of finding one or enumerating them have already been solved in a satisfactory way. In this paper, the following related problem is studied: given a family T of trees, all having the same vertex set V, determine whether there exists a chordal graph whose set of clique trees equals T. For that purpose, we undertake a study of the structural properties, some already known and some new, of the clique trees of a chordal graph and the characteristics of the sets that induce subtrees of every clique tree. Some necessary and sufficient conditions and examples of how they can be applied are found, eventually establishing that a positive or negative answer to the problem can be obtained in polynomial time. If affirmative, a graph whose set of clique trees equals T is also obtained. Finally, all the chordal graphs with set of clique trees equal to T are characterized. |
| publishDate |
2011 |
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2011-11-22 |
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eng |
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eng |
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