The clique operator on circular-arc graphs

Autores
Lin, M.C.; Soulignac, F.J.; Szwarcfiter, J.L.
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A circular-arc graphG is the intersection graph of a collection of arcs on the circle and such a collection is called a model of G. Say that the model is proper when no arc of the collection contains another one, it is Helly when the arcs satisfy the Helly Property, while the model is proper Helly when it is simultaneously proper and Helly. A graph admitting a Helly (resp. proper Helly) model is called a Helly (resp. proper Helly) circular-arc graph. The clique graphK (G) of a graph G is the intersection graph of its cliques. The iterated clique graphKi (G) of G is defined by K0 (G) = G and Ki + 1 (G) = K (Ki (G)). In this paper, we consider two problems on clique graphs of circular-arc graphs. The first is to characterize clique graphs of Helly circular-arc graphs and proper Helly circular-arc graphs. The second is to characterize the graph to which a general circular-arc graph K-converges, if it is K-convergent. We propose complete solutions to both problems, extending the partial results known so far. The methods lead to linear time recognition algorithms, for both problems. © 2009 Elsevier B.V. All rights reserved.
Fil:Lin, M.C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Soulignac, F.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente
Discrete Appl Math 2010;158(12):1259-1267
Materia
Algorithms
Clique graphs
Helly circular-arc graphs
K-behavior
Proper Helly circular-arc graphs
Circular-arc graph
Clique graphs
Complete solutions
Graph G
Intersection graph
K-behavior
Linear time
Recognition algorithm
Algorithms
Graph theory
Mathematical operators
Graphic methods
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_0166218X_v158_n12_p1259_Lin
Acceder
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oai_identifier_str paperaa:paper_0166218X_v158_n12_p1259_Lin
network_acronym_str BDUBAFCEN
repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling The clique operator on circular-arc graphsLin, M.C.Soulignac, F.J.Szwarcfiter, J.L.AlgorithmsClique graphsHelly circular-arc graphsK-behaviorProper Helly circular-arc graphsCircular-arc graphClique graphsComplete solutionsGraph GIntersection graphK-behaviorLinear timeRecognition algorithmAlgorithmsGraph theoryMathematical operatorsGraphic methodsA circular-arc graphG is the intersection graph of a collection of arcs on the circle and such a collection is called a model of G. Say that the model is proper when no arc of the collection contains another one, it is Helly when the arcs satisfy the Helly Property, while the model is proper Helly when it is simultaneously proper and Helly. A graph admitting a Helly (resp. proper Helly) model is called a Helly (resp. proper Helly) circular-arc graph. The clique graphK (G) of a graph G is the intersection graph of its cliques. The iterated clique graphKi (G) of G is defined by K0 (G) = G and Ki + 1 (G) = K (Ki (G)). In this paper, we consider two problems on clique graphs of circular-arc graphs. The first is to characterize clique graphs of Helly circular-arc graphs and proper Helly circular-arc graphs. The second is to characterize the graph to which a general circular-arc graph K-converges, if it is K-convergent. We propose complete solutions to both problems, extending the partial results known so far. The methods lead to linear time recognition algorithms, for both problems. © 2009 Elsevier B.V. All rights reserved.Fil:Lin, M.C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Soulignac, F.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2010info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_0166218X_v158_n12_p1259_LinDiscrete Appl Math 2010;158(12):1259-1267reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-09-04T09:48:21Zpaperaa:paper_0166218X_v158_n12_p1259_LinInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-09-04 09:48:22.532Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv The clique operator on circular-arc graphs
title The clique operator on circular-arc graphs
spellingShingle The clique operator on circular-arc graphs
Lin, M.C.
Algorithms
Clique graphs
Helly circular-arc graphs
K-behavior
Proper Helly circular-arc graphs
Circular-arc graph
Clique graphs
Complete solutions
Graph G
Intersection graph
K-behavior
Linear time
Recognition algorithm
Algorithms
Graph theory
Mathematical operators
Graphic methods
title_short The clique operator on circular-arc graphs
title_full The clique operator on circular-arc graphs
title_fullStr The clique operator on circular-arc graphs
title_full_unstemmed The clique operator on circular-arc graphs
title_sort The clique operator on circular-arc graphs
dc.creator.none.fl_str_mv Lin, M.C.
Soulignac, F.J.
Szwarcfiter, J.L.
author Lin, M.C.
author_facet Lin, M.C.
Soulignac, F.J.
Szwarcfiter, J.L.
author_role author
author2 Soulignac, F.J.
Szwarcfiter, J.L.
author2_role author
author
dc.subject.none.fl_str_mv Algorithms
Clique graphs
Helly circular-arc graphs
K-behavior
Proper Helly circular-arc graphs
Circular-arc graph
Clique graphs
Complete solutions
Graph G
Intersection graph
K-behavior
Linear time
Recognition algorithm
Algorithms
Graph theory
Mathematical operators
Graphic methods
topic Algorithms
Clique graphs
Helly circular-arc graphs
K-behavior
Proper Helly circular-arc graphs
Circular-arc graph
Clique graphs
Complete solutions
Graph G
Intersection graph
K-behavior
Linear time
Recognition algorithm
Algorithms
Graph theory
Mathematical operators
Graphic methods
dc.description.none.fl_txt_mv A circular-arc graphG is the intersection graph of a collection of arcs on the circle and such a collection is called a model of G. Say that the model is proper when no arc of the collection contains another one, it is Helly when the arcs satisfy the Helly Property, while the model is proper Helly when it is simultaneously proper and Helly. A graph admitting a Helly (resp. proper Helly) model is called a Helly (resp. proper Helly) circular-arc graph. The clique graphK (G) of a graph G is the intersection graph of its cliques. The iterated clique graphKi (G) of G is defined by K0 (G) = G and Ki + 1 (G) = K (Ki (G)). In this paper, we consider two problems on clique graphs of circular-arc graphs. The first is to characterize clique graphs of Helly circular-arc graphs and proper Helly circular-arc graphs. The second is to characterize the graph to which a general circular-arc graph K-converges, if it is K-convergent. We propose complete solutions to both problems, extending the partial results known so far. The methods lead to linear time recognition algorithms, for both problems. © 2009 Elsevier B.V. All rights reserved.
Fil:Lin, M.C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Soulignac, F.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
description A circular-arc graphG is the intersection graph of a collection of arcs on the circle and such a collection is called a model of G. Say that the model is proper when no arc of the collection contains another one, it is Helly when the arcs satisfy the Helly Property, while the model is proper Helly when it is simultaneously proper and Helly. A graph admitting a Helly (resp. proper Helly) model is called a Helly (resp. proper Helly) circular-arc graph. The clique graphK (G) of a graph G is the intersection graph of its cliques. The iterated clique graphKi (G) of G is defined by K0 (G) = G and Ki + 1 (G) = K (Ki (G)). In this paper, we consider two problems on clique graphs of circular-arc graphs. The first is to characterize clique graphs of Helly circular-arc graphs and proper Helly circular-arc graphs. The second is to characterize the graph to which a general circular-arc graph K-converges, if it is K-convergent. We propose complete solutions to both problems, extending the partial results known so far. The methods lead to linear time recognition algorithms, for both problems. © 2009 Elsevier B.V. All rights reserved.
publishDate 2010
dc.date.none.fl_str_mv 2010
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/20.500.12110/paper_0166218X_v158_n12_p1259_Lin
url http://hdl.handle.net/20.500.12110/paper_0166218X_v158_n12_p1259_Lin
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Discrete Appl Math 2010;158(12):1259-1267
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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