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

Autores
Alcón, Liliana Graciela; Gutierrez, 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.
Fil: Alcón, Liliana Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Gutierrez, Marisa. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Materia
CHORDAL GRAPHS
CLIQUE-TREE
HELLY CIRCULAR-ARC GRAPHS
INTERSECTION MODELS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/198122
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Finding intersection models: From chordal to Helly circular-arc graphsAlcón, Liliana GracielaGutierrez, MarisaCHORDAL GRAPHSCLIQUE-TREEHELLY CIRCULAR-ARC GRAPHSINTERSECTION MODELShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Every 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.Fil: Alcón, Liliana Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: Gutierrez, Marisa. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaElsevier Science2012-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/198122Alcón, Liliana Graciela; Gutierrez, Marisa; Finding intersection models: From chordal to Helly circular-arc graphs; Elsevier Science; Discrete Mathematics; 312; 6; 3-2012; 1148-11570012-365XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0012365X11005437info:eu-repo/semantics/altIdentifier/doi/10.1016/j.disc.2011.11.036info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:54:24Zoai:ri.conicet.gov.ar:11336/198122instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:54:24.761CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
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
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
Gutierrez, Marisa
author Alcón, Liliana Graciela
author_facet Alcón, Liliana Graciela
Gutierrez, Marisa
author_role author
author2 Gutierrez, Marisa
author2_role author
dc.subject.none.fl_str_mv CHORDAL GRAPHS
CLIQUE-TREE
HELLY CIRCULAR-ARC GRAPHS
INTERSECTION MODELS
topic CHORDAL GRAPHS
CLIQUE-TREE
HELLY CIRCULAR-ARC GRAPHS
INTERSECTION MODELS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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.
Fil: Alcón, Liliana Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Gutierrez, Marisa. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
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 2012-03
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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://hdl.handle.net/11336/198122
Alcón, Liliana Graciela; Gutierrez, Marisa; Finding intersection models: From chordal to Helly circular-arc graphs; Elsevier Science; Discrete Mathematics; 312; 6; 3-2012; 1148-1157
0012-365X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/198122
identifier_str_mv Alcón, Liliana Graciela; Gutierrez, Marisa; Finding intersection models: From chordal to Helly circular-arc graphs; Elsevier Science; Discrete Mathematics; 312; 6; 3-2012; 1148-1157
0012-365X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0012365X11005437
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.disc.2011.11.036
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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