A Characterization of Claw-free CIS Graphs and New Results on the Order of CIS Graphs

Autores
Alcón, Liliana Graciela; Gutiérrez, Marisa; Milanič, Martin
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
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.
Facultad de Ciencias Exactas
Materia
Matemática
CIS graph
Maximal clique
Maximal stable set
Maximal independent set
Randomly internally matchable graph
Claw-free graph
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/103273
Acceder
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network_name_str SEDICI (UNLP)
spelling A Characterization of Claw-free CIS Graphs and New Results on the Order of CIS GraphsAlcón, Liliana GracielaGutiérrez, MarisaMilanič, MartinMatemáticaCIS graphMaximal cliqueMaximal stable setMaximal independent setRandomly internally matchable graphClaw-free graphA 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.Facultad de Ciencias Exactas2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf15-27http://sedici.unlp.edu.ar/handle/10915/103273enginfo:eu-repo/semantics/altIdentifier/issn/1571-0661info:eu-repo/semantics/altIdentifier/doi/10.1016/j.entcs.2019.08.003info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-15T11:14:19Zoai:sedici.unlp.edu.ar:10915/103273Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-15 11:14:19.933SEDICI (UNLP) - Universidad Nacional de La Platafalse
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
Matemática
CIS graph
Maximal clique
Maximal stable set
Maximal independent set
Randomly internally matchable graph
Claw-free graph
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
Gutiérrez, Marisa
Milanič, Martin
author Alcón, Liliana Graciela
author_facet Alcón, Liliana Graciela
Gutiérrez, Marisa
Milanič, Martin
author_role author
author2 Gutiérrez, Marisa
Milanič, Martin
author2_role author
author
dc.subject.none.fl_str_mv Matemática
CIS graph
Maximal clique
Maximal stable set
Maximal independent set
Randomly internally matchable graph
Claw-free graph
topic Matemática
CIS graph
Maximal clique
Maximal stable set
Maximal independent set
Randomly internally matchable graph
Claw-free graph
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.
Facultad de Ciencias Exactas
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/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/103273
url http://sedici.unlp.edu.ar/handle/10915/103273
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/1571-0661
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.entcs.2019.08.003
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
15-27
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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