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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/129763
Ver los metadatos del registro completo
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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 Técnicas2025-09-03T09:50:47Zoai: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:34982025-09-03 09:50:47.619CONICET 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 |
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https://creativecommons.org/licenses/by-nc-nd/2.5/ar/ |
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Elsevier Science |
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Elsevier Science |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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