A characterization of claw-free CIS graphs and new results on the order of CIS graphs

Autores
Alcón, Liliana Graciela; Gutierrez, Marisa; Milanic, Martin
Año de publicación
2019
Idioma
inglés
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
A graph is CIS if every maximal clique interesects every maximal stable set. Currently, no good characterization or recognition algorithm for the CIS graphs is known. We characterize graphs in which every maximal matching saturates all vertices of degree at least two and use this result to give a structural, efficiently testable characterization of claw-free CIS graphs. We answer in the negative a question of Dobson, Hujdurović, Milanič, and Verret [Vertex-transitive CIS graphs, European J. Combin. 44 (2015) 87–98] asking whether the number of vertices of every CIS graph is bounded from above by the product of its clique and stability numbers. On the positive side, we show that the question of Dobson et al. has an affirmative answer in the case of claw-free graphs.
Fil: Alcón, Liliana Graciela. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Gutierrez, Marisa. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Milanic, Martin. Univerza Na Primorskem.; Eslovenia
Lagos 2019, the tenth Latin and American Algorithms, Graphs and Optimization Symposium
Belo Horizonte
Brasil
Latin and American Algorithms, Graphs and Optimization Symposium
Materia
maximal clique
maximal estable set
CIS 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:11336/129763
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/129763
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A characterization of claw-free CIS graphs and new results on the order of CIS graphsAlcón, Liliana GracielaGutierrez, MarisaMilanic, Martinmaximal cliquemaximal estable setCIS graphshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A graph is CIS if every maximal clique interesects every maximal stable set. Currently, no good characterization or recognition algorithm for the CIS graphs is known. We characterize graphs in which every maximal matching saturates all vertices of degree at least two and use this result to give a structural, efficiently testable characterization of claw-free CIS graphs. We answer in the negative a question of Dobson, Hujdurović, Milanič, and Verret [Vertex-transitive CIS graphs, European J. Combin. 44 (2015) 87–98] asking whether the number of vertices of every CIS graph is bounded from above by the product of its clique and stability numbers. On the positive side, we show that the question of Dobson et al. has an affirmative answer in the case of claw-free graphs.Fil: Alcón, Liliana Graciela. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Gutierrez, Marisa. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Milanic, Martin. Univerza Na Primorskem.; EsloveniaLagos 2019, the tenth Latin and American Algorithms, Graphs and Optimization SymposiumBelo HorizonteBrasilLatin and American Algorithms, Graphs and Optimization SymposiumElsevier ScienceCoutinho. GabrielKohayakawa, YoshiharuSantos, Vinicius dosUrrutia, Sebastián2019info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObjectSimposioJournalhttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/129763A characterization of claw-free CIS graphs and new results on the order of CIS graphs; Lagos 2019, the tenth Latin and American Algorithms, Graphs and Optimization Symposium; Belo Horizonte; Brasil; 2019; 15-271571-0653CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S1571066119300532info:eu-repo/semantics/altIdentifier/doi/10.1016/j.entcs.2019.08.003info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1812.05314Internacionalinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:46:13Zoai:ri.conicet.gov.ar:11336/129763instacron: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:34982025-09-29 09:46:13.367CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A characterization of claw-free CIS graphs and new results on the order of CIS graphs
title A characterization of claw-free CIS graphs and new results on the order of CIS graphs
spellingShingle A characterization of claw-free CIS graphs and new results on the order of CIS graphs
Alcón, Liliana Graciela
maximal clique
maximal estable set
CIS graphs
title_short A characterization of claw-free CIS graphs and new results on the order of CIS graphs
title_full A characterization of claw-free CIS graphs and new results on the order of CIS graphs
title_fullStr A characterization of claw-free CIS graphs and new results on the order of CIS graphs
title_full_unstemmed A characterization of claw-free CIS graphs and new results on the order of CIS graphs
title_sort A characterization of claw-free CIS graphs and new results on the order of CIS graphs
dc.creator.none.fl_str_mv Alcón, Liliana Graciela
Gutierrez, Marisa
Milanic, Martin
author Alcón, Liliana Graciela
author_facet Alcón, Liliana Graciela
Gutierrez, Marisa
Milanic, Martin
author_role author
author2 Gutierrez, Marisa
Milanic, Martin
author2_role author
author
dc.contributor.none.fl_str_mv Coutinho. Gabriel
Kohayakawa, Yoshiharu
Santos, Vinicius dos
Urrutia, Sebastián
dc.subject.none.fl_str_mv maximal clique
maximal estable set
CIS graphs
topic maximal clique
maximal estable set
CIS 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 graph is CIS if every maximal clique interesects every maximal stable set. Currently, no good characterization or recognition algorithm for the CIS graphs is known. We characterize graphs in which every maximal matching saturates all vertices of degree at least two and use this result to give a structural, efficiently testable characterization of claw-free CIS graphs. We answer in the negative a question of Dobson, Hujdurović, Milanič, and Verret [Vertex-transitive CIS graphs, European J. Combin. 44 (2015) 87–98] asking whether the number of vertices of every CIS graph is bounded from above by the product of its clique and stability numbers. On the positive side, we show that the question of Dobson et al. has an affirmative answer in the case of claw-free graphs.
Fil: Alcón, Liliana Graciela. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Gutierrez, Marisa. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Milanic, Martin. Univerza Na Primorskem.; Eslovenia
Lagos 2019, the tenth Latin and American Algorithms, Graphs and Optimization Symposium
Belo Horizonte
Brasil
Latin and American Algorithms, Graphs and Optimization Symposium
description A graph is CIS if every maximal clique interesects every maximal stable set. Currently, no good characterization or recognition algorithm for the CIS graphs is known. We characterize graphs in which every maximal matching saturates all vertices of degree at least two and use this result to give a structural, efficiently testable characterization of claw-free CIS graphs. We answer in the negative a question of Dobson, Hujdurović, Milanič, and Verret [Vertex-transitive CIS graphs, European J. Combin. 44 (2015) 87–98] asking whether the number of vertices of every CIS graph is bounded from above by the product of its clique and stability numbers. On the positive side, we show that the question of Dobson et al. has an affirmative answer in the case of claw-free graphs.
publishDate 2019
dc.date.none.fl_str_mv 2019
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/conferenceObject
Simposio
Journal
http://purl.org/coar/resource_type/c_5794
info:ar-repo/semantics/documentoDeConferencia
status_str publishedVersion
format conferenceObject
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/129763
A characterization of claw-free CIS graphs and new results on the order of CIS graphs; Lagos 2019, the tenth Latin and American Algorithms, Graphs and Optimization Symposium; Belo Horizonte; Brasil; 2019; 15-27
1571-0653
CONICET Digital
CONICET
url http://hdl.handle.net/11336/129763
identifier_str_mv A characterization of claw-free CIS graphs and new results on the order of CIS graphs; Lagos 2019, the tenth Latin and American Algorithms, Graphs and Optimization Symposium; Belo Horizonte; Brasil; 2019; 15-27
1571-0653
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/S1571066119300532
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.entcs.2019.08.003
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1812.05314
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.coverage.none.fl_str_mv Internacional
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 13.070432

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