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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/102919
Ver los metadatos del registro completo
id |
SEDICI_051a8b68f6e410aa5baef99ee02ef7f3 |
---|---|
oai_identifier_str |
oai:sedici.unlp.edu.ar:10915/102919 |
network_acronym_str |
SEDICI |
repository_id_str |
1329 |
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:UNLP2025-09-03T10:54:29Zoai: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:13292025-09-03 10:54:30.005SEDICI (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 |
_version_ |
1842260431230468096 |
score |
13.13397 |