Finding intersection models: From chordal to Helly circular-arc graphs

Autores
Alcón, Liliana Graciela; Gutiérrez, Marisa
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Every chordal graph G admits a representation as the intersection graph of a family of subtrees of a tree. A classic way of finding such an intersection model is to look for a maximum spanning tree of the valuated clique graph of G. Similar techniques have been applied to find intersection models of chordal graph subclasses as interval graphs and path graphs. In this work, we extend those methods to be applied beyond chordal graphs: we prove that a graph G can be represented as the intersection of a Helly separating family of graphs belonging to a given class if and only if there exists a spanning subgraph of the clique graph of G satisfying a particular condition. Moreover, such a spanning subgraph is characterized by its weight in the valuated clique graph of G. The specific case of Helly circular-arc graphs is treated. We show that the canonical intersection models of those graphs correspond to the maximum spanning cycles of the valuated clique graph.
Facultad de Ciencias Exactas
Materia
Matemática
Chordal graphs
Clique-tree
Helly circular-arc graphs
Intersection models
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/84095
Acceder
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network_name_str SEDICI (UNLP)
spelling Finding intersection models: From chordal to Helly circular-arc graphsAlcón, Liliana GracielaGutiérrez, MarisaMatemáticaChordal graphsClique-treeHelly circular-arc graphsIntersection modelsEvery chordal graph G admits a representation as the intersection graph of a family of subtrees of a tree. A classic way of finding such an intersection model is to look for a maximum spanning tree of the valuated clique graph of G. Similar techniques have been applied to find intersection models of chordal graph subclasses as interval graphs and path graphs. In this work, we extend those methods to be applied beyond chordal graphs: we prove that a graph G can be represented as the intersection of a Helly separating family of graphs belonging to a given class if and only if there exists a spanning subgraph of the clique graph of G satisfying a particular condition. Moreover, such a spanning subgraph is characterized by its weight in the valuated clique graph of G. The specific case of Helly circular-arc graphs is treated. We show that the canonical intersection models of those graphs correspond to the maximum spanning cycles of the valuated clique graph.Facultad de Ciencias Exactas2012info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf1148-1157http://sedici.unlp.edu.ar/handle/10915/84095enginfo:eu-repo/semantics/altIdentifier/issn/0012-365Xinfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.disc.2011.11.036info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-03T10:48:20Zoai:sedici.unlp.edu.ar:10915/84095Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-03 10:48:20.487SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Finding intersection models: From chordal to Helly circular-arc graphs
title Finding intersection models: From chordal to Helly circular-arc graphs
spellingShingle Finding intersection models: From chordal to Helly circular-arc graphs
Alcón, Liliana Graciela
Matemática
Chordal graphs
Clique-tree
Helly circular-arc graphs
Intersection models
title_short Finding intersection models: From chordal to Helly circular-arc graphs
title_full Finding intersection models: From chordal to Helly circular-arc graphs
title_fullStr Finding intersection models: From chordal to Helly circular-arc graphs
title_full_unstemmed Finding intersection models: From chordal to Helly circular-arc graphs
title_sort Finding intersection models: From chordal to Helly circular-arc graphs
dc.creator.none.fl_str_mv Alcón, Liliana Graciela
Gutiérrez, Marisa
author Alcón, Liliana Graciela
author_facet Alcón, Liliana Graciela
Gutiérrez, Marisa
author_role author
author2 Gutiérrez, Marisa
author2_role author
dc.subject.none.fl_str_mv Matemática
Chordal graphs
Clique-tree
Helly circular-arc graphs
Intersection models
topic Matemática
Chordal graphs
Clique-tree
Helly circular-arc graphs
Intersection models
dc.description.none.fl_txt_mv Every chordal graph G admits a representation as the intersection graph of a family of subtrees of a tree. A classic way of finding such an intersection model is to look for a maximum spanning tree of the valuated clique graph of G. Similar techniques have been applied to find intersection models of chordal graph subclasses as interval graphs and path graphs. In this work, we extend those methods to be applied beyond chordal graphs: we prove that a graph G can be represented as the intersection of a Helly separating family of graphs belonging to a given class if and only if there exists a spanning subgraph of the clique graph of G satisfying a particular condition. Moreover, such a spanning subgraph is characterized by its weight in the valuated clique graph of G. The specific case of Helly circular-arc graphs is treated. We show that the canonical intersection models of those graphs correspond to the maximum spanning cycles of the valuated clique graph.
Facultad de Ciencias Exactas
description Every chordal graph G admits a representation as the intersection graph of a family of subtrees of a tree. A classic way of finding such an intersection model is to look for a maximum spanning tree of the valuated clique graph of G. Similar techniques have been applied to find intersection models of chordal graph subclasses as interval graphs and path graphs. In this work, we extend those methods to be applied beyond chordal graphs: we prove that a graph G can be represented as the intersection of a Helly separating family of graphs belonging to a given class if and only if there exists a spanning subgraph of the clique graph of G satisfying a particular condition. Moreover, such a spanning subgraph is characterized by its weight in the valuated clique graph of G. The specific case of Helly circular-arc graphs is treated. We show that the canonical intersection models of those graphs correspond to the maximum spanning cycles of the valuated clique graph.
publishDate 2012
dc.date.none.fl_str_mv 2012
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/84095
url http://sedici.unlp.edu.ar/handle/10915/84095
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0012-365X
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.disc.2011.11.036
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
1148-1157
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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