The clique operator on circular-arc graphs

Autores
Lin, Min Chih; Soulignac, Francisco Juan; Szwarcfiter, Jayme 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.
Fil: Lin, Min Chih. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Fil: Soulignac, Francisco Juan. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; Brasil
Materia
ALGORITHMS
CLIQUE GRAPHS
HELLY CIRCULAR-ARC GRAPHS
K-BEHAVIOR
PROPER HELLY CIRCULAR-ARC GRAPHS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/98696
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/98696
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling The clique operator on circular-arc graphsLin, Min ChihSoulignac, Francisco JuanSzwarcfiter, Jayme L.ALGORITHMSCLIQUE GRAPHSHELLY CIRCULAR-ARC GRAPHSK-BEHAVIORPROPER HELLY CIRCULAR-ARC GRAPHShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A 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.Fil: Lin, Min Chih. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Soulignac, Francisco Juan. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; BrasilElsevier Science2010-06info: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/11336/98696Lin, Min Chih; Soulignac, Francisco Juan; Szwarcfiter, Jayme L.; The clique operator on circular-arc graphs; Elsevier Science; Discrete Applied Mathematics; 158; 12; 6-2010; 1259-12670166-218XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2009.01.019info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0166218X09000195info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:56:09Zoai:ri.conicet.gov.ar:11336/98696instacron: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 09:56:09.344CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
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, Min Chih
ALGORITHMS
CLIQUE GRAPHS
HELLY CIRCULAR-ARC GRAPHS
K-BEHAVIOR
PROPER HELLY CIRCULAR-ARC GRAPHS
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, Min Chih
Soulignac, Francisco Juan
Szwarcfiter, Jayme L.
author Lin, Min Chih
author_facet Lin, Min Chih
Soulignac, Francisco Juan
Szwarcfiter, Jayme L.
author_role author
author2 Soulignac, Francisco Juan
Szwarcfiter, Jayme 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
topic ALGORITHMS
CLIQUE GRAPHS
HELLY CIRCULAR-ARC GRAPHS
K-BEHAVIOR
PROPER HELLY CIRCULAR-ARC GRAPHS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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.
Fil: Lin, Min Chih. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Fil: Soulignac, Francisco Juan. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; Brasil
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.
publishDate 2010
dc.date.none.fl_str_mv 2010-06
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/11336/98696
Lin, Min Chih; Soulignac, Francisco Juan; Szwarcfiter, Jayme L.; The clique operator on circular-arc graphs; Elsevier Science; Discrete Applied Mathematics; 158; 12; 6-2010; 1259-1267
0166-218X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/98696
identifier_str_mv Lin, Min Chih; Soulignac, Francisco Juan; Szwarcfiter, Jayme L.; The clique operator on circular-arc graphs; Elsevier Science; Discrete Applied Mathematics; 158; 12; 6-2010; 1259-1267
0166-218X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2009.01.019
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0166218X09000195
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/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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