Helly EPT graphs on bounded degree trees : Characterization and recognition

Autores
Alcón, Liliana Graciela; Gutiérrez, Marisa; Mazzoleni, María Pía
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The edge-intersection graph of a family of paths on a host tree is called an EPT graph. When the tree has maximum degree h, we say that the graph is [h, 2, 2]. If, in addition, the family of paths satisfies the Helly property, then the graph is Helly [h, 2, 2]. In this paper, we present a family of EPT graphs called gates which are forbidden induced subgraphs for [h, 2, 2] graphs. Using these we characterize by forbidden induced subgraphs the Helly [h, 2, 2] graphs. As a byproduct we prove that in getting a Helly EPT -representation, it is not necessary to increase the maximum degree of the host tree. In addition, we give an efficient algorithm to recognize Helly [h, 2, 2] graphs based on their decomposition by maximal clique separators.
Departamento de Matemática
Materia
Matemática
Intersection graphs
EPT graphs
Tolerance graphs
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:10915/102919
Acceder
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network_acronym_str SEDICI
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network_name_str SEDICI (UNLP)
spelling Helly EPT graphs on bounded degree trees : Characterization and recognitionAlcón, Liliana GracielaGutiérrez, MarisaMazzoleni, María PíaMatemáticaIntersection graphsEPT graphsTolerance graphsThe edge-intersection graph of a family of paths on a host tree is called an <i>EPT</i> graph. When the tree has maximum degree h, we say that the graph is [<i>h</i>, 2, 2]. If, in addition, the family of paths satisfies the Helly property, then the graph is Helly [<i>h</i>, 2, 2]. In this paper, we present a family of <i>EPT</i> graphs called gates which are forbidden induced subgraphs for [<i>h</i>, 2, 2] graphs. Using these we characterize by forbidden induced subgraphs the Helly [<i>h</i>, 2, 2] graphs. As a byproduct we prove that in getting a Helly <i>EPT</i> -representation, it is not necessary to increase the maximum degree of the host tree. In addition, we give an efficient algorithm to recognize Helly [<i>h</i>, 2, 2] graphs based on their decomposition by maximal clique separators.Departamento de Matemática2017-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf2798 - 2806http://sedici.unlp.edu.ar/handle/10915/102919enginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0012365X17302571?via%3Dihubinfo:eu-repo/semantics/altIdentifier/issn/0012-365Xinfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.disc.2017.08.011info: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:UNLP2025-09-29T11:22:18Zoai:sedici.unlp.edu.ar:10915/102919Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:22:18.676SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Helly EPT graphs on bounded degree trees : Characterization and recognition
title Helly EPT graphs on bounded degree trees : Characterization and recognition
spellingShingle Helly EPT graphs on bounded degree trees : Characterization and recognition
Alcón, Liliana Graciela
Matemática
Intersection graphs
EPT graphs
Tolerance graphs
title_short Helly EPT graphs on bounded degree trees : Characterization and recognition
title_full Helly EPT graphs on bounded degree trees : Characterization and recognition
title_fullStr Helly EPT graphs on bounded degree trees : Characterization and recognition
title_full_unstemmed Helly EPT graphs on bounded degree trees : Characterization and recognition
title_sort Helly EPT graphs on bounded degree trees : Characterization and recognition
dc.creator.none.fl_str_mv Alcón, Liliana Graciela
Gutiérrez, Marisa
Mazzoleni, María Pía
author Alcón, Liliana Graciela
author_facet Alcón, Liliana Graciela
Gutiérrez, Marisa
Mazzoleni, María Pía
author_role author
author2 Gutiérrez, Marisa
Mazzoleni, María Pía
author2_role author
author
dc.subject.none.fl_str_mv Matemática
Intersection graphs
EPT graphs
Tolerance graphs
topic Matemática
Intersection graphs
EPT graphs
Tolerance graphs
dc.description.none.fl_txt_mv The edge-intersection graph of a family of paths on a host tree is called an <i>EPT</i> graph. When the tree has maximum degree h, we say that the graph is [<i>h</i>, 2, 2]. If, in addition, the family of paths satisfies the Helly property, then the graph is Helly [<i>h</i>, 2, 2]. In this paper, we present a family of <i>EPT</i> graphs called gates which are forbidden induced subgraphs for [<i>h</i>, 2, 2] graphs. Using these we characterize by forbidden induced subgraphs the Helly [<i>h</i>, 2, 2] graphs. As a byproduct we prove that in getting a Helly <i>EPT</i> -representation, it is not necessary to increase the maximum degree of the host tree. In addition, we give an efficient algorithm to recognize Helly [<i>h</i>, 2, 2] graphs based on their decomposition by maximal clique separators.
Departamento de Matemática
description The edge-intersection graph of a family of paths on a host tree is called an <i>EPT</i> graph. When the tree has maximum degree h, we say that the graph is [<i>h</i>, 2, 2]. If, in addition, the family of paths satisfies the Helly property, then the graph is Helly [<i>h</i>, 2, 2]. In this paper, we present a family of <i>EPT</i> graphs called gates which are forbidden induced subgraphs for [<i>h</i>, 2, 2] graphs. Using these we characterize by forbidden induced subgraphs the Helly [<i>h</i>, 2, 2] graphs. As a byproduct we prove that in getting a Helly <i>EPT</i> -representation, it is not necessary to increase the maximum degree of the host tree. In addition, we give an efficient algorithm to recognize Helly [<i>h</i>, 2, 2] graphs based on their decomposition by maximal clique separators.
publishDate 2017
dc.date.none.fl_str_mv 2017-12
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/10915/102919
url http://sedici.unlp.edu.ar/handle/10915/102919
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/abs/pii/S0012365X17302571?via%3Dihub
info:eu-repo/semantics/altIdentifier/issn/0012-365X
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.disc.2017.08.011
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
2798 - 2806
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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score 13.070432

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