A note on Helly-B1-EPG graphs

Autores
Alcón, Liliana Graciela; Mazzoleni, María Pía; Dias Dos Santos, Tanilson
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Edge intersection graphs of paths on a grid (EPG graphs) aregraphs whose vertices can be represented as nontrivial paths on agrid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. When the paths haveat most one change of direction (bend) these graphs are called B1-EPG graphs. In this paper, we delimit some subclasses of B1-EPGgraphs that admit a Helly-B1-EPG representation. It is known thatB1-EPG and Helly-B1-EPG are hereditary classes, so they can becharacterized by forbidden structures. In both cases, finding thewhole list of minimal forbidden induced subgraphs are challengingopen problems. Taking a step towards solving those problems, wedescribe a few structures at least one of which will necessarily bepresent in any B1-EPG graph that does not admit a Helly representation. In addition, we show that the well known families of Blockgraphs, Cactus and Line of Bipartite graphs are totally contained inthe class Helly-B1-EPG.
Fil: Alcón, Liliana Graciela. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Fil: Mazzoleni, María Pía. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Fil: Dias Dos Santos, Tanilson. Universidade Federal do Rio de Janeiro; Brasil
Materia
EDGE- INYTERSECTION GRAPHS OF PATHS ON A GRID
HELLY PROPERTY
SINGLE BEND PATHS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/160294
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A note on Helly-B1-EPG graphsAlcón, Liliana GracielaMazzoleni, María PíaDias Dos Santos, TanilsonEDGE- INYTERSECTION GRAPHS OF PATHS ON A GRIDHELLY PROPERTYSINGLE BEND PATHShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Edge intersection graphs of paths on a grid (EPG graphs) aregraphs whose vertices can be represented as nontrivial paths on agrid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. When the paths haveat most one change of direction (bend) these graphs are called B1-EPG graphs. In this paper, we delimit some subclasses of B1-EPGgraphs that admit a Helly-B1-EPG representation. It is known thatB1-EPG and Helly-B1-EPG are hereditary classes, so they can becharacterized by forbidden structures. In both cases, finding thewhole list of minimal forbidden induced subgraphs are challengingopen problems. Taking a step towards solving those problems, wedescribe a few structures at least one of which will necessarily bepresent in any B1-EPG graph that does not admit a Helly representation. In addition, we show that the well known families of Blockgraphs, Cactus and Line of Bipartite graphs are totally contained inthe class Helly-B1-EPG.Fil: Alcón, Liliana Graciela. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaFil: Mazzoleni, María Pía. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaFil: Dias Dos Santos, Tanilson. Universidade Federal do Rio de Janeiro; BrasilSociedad Brasilera de Matemàtica2021-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/160294Alcón, Liliana Graciela; Mazzoleni, María Pía; Dias Dos Santos, Tanilson; A note on Helly-B1-EPG graphs; Sociedad Brasilera de Matemàtica; Matemática Contemporânea; 48; 10-2021; 22-300103-9059CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.21711/231766362021/rmc483info:eu-repo/semantics/altIdentifier/url/https://mc.sbm.org.br/wp-content/uploads/sites/9/sites/9/2022/01/Article-03-vol-48.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:42:15Zoai:ri.conicet.gov.ar:11336/160294instacron: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 09:42:16.261CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A note on Helly-B1-EPG graphs
title A note on Helly-B1-EPG graphs
spellingShingle A note on Helly-B1-EPG graphs
Alcón, Liliana Graciela
EDGE- INYTERSECTION GRAPHS OF PATHS ON A GRID
HELLY PROPERTY
SINGLE BEND PATHS
title_short A note on Helly-B1-EPG graphs
title_full A note on Helly-B1-EPG graphs
title_fullStr A note on Helly-B1-EPG graphs
title_full_unstemmed A note on Helly-B1-EPG graphs
title_sort A note on Helly-B1-EPG graphs
dc.creator.none.fl_str_mv Alcón, Liliana Graciela
Mazzoleni, María Pía
Dias Dos Santos, Tanilson
author Alcón, Liliana Graciela
author_facet Alcón, Liliana Graciela
Mazzoleni, María Pía
Dias Dos Santos, Tanilson
author_role author
author2 Mazzoleni, María Pía
Dias Dos Santos, Tanilson
author2_role author
author
dc.subject.none.fl_str_mv EDGE- INYTERSECTION GRAPHS OF PATHS ON A GRID
HELLY PROPERTY
SINGLE BEND PATHS
topic EDGE- INYTERSECTION GRAPHS OF PATHS ON A GRID
HELLY PROPERTY
SINGLE BEND PATHS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Edge intersection graphs of paths on a grid (EPG graphs) aregraphs whose vertices can be represented as nontrivial paths on agrid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. When the paths haveat most one change of direction (bend) these graphs are called B1-EPG graphs. In this paper, we delimit some subclasses of B1-EPGgraphs that admit a Helly-B1-EPG representation. It is known thatB1-EPG and Helly-B1-EPG are hereditary classes, so they can becharacterized by forbidden structures. In both cases, finding thewhole list of minimal forbidden induced subgraphs are challengingopen problems. Taking a step towards solving those problems, wedescribe a few structures at least one of which will necessarily bepresent in any B1-EPG graph that does not admit a Helly representation. In addition, we show that the well known families of Blockgraphs, Cactus and Line of Bipartite graphs are totally contained inthe class Helly-B1-EPG.
Fil: Alcón, Liliana Graciela. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Fil: Mazzoleni, María Pía. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Fil: Dias Dos Santos, Tanilson. Universidade Federal do Rio de Janeiro; Brasil
description Edge intersection graphs of paths on a grid (EPG graphs) aregraphs whose vertices can be represented as nontrivial paths on agrid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. When the paths haveat most one change of direction (bend) these graphs are called B1-EPG graphs. In this paper, we delimit some subclasses of B1-EPGgraphs that admit a Helly-B1-EPG representation. It is known thatB1-EPG and Helly-B1-EPG are hereditary classes, so they can becharacterized by forbidden structures. In both cases, finding thewhole list of minimal forbidden induced subgraphs are challengingopen problems. Taking a step towards solving those problems, wedescribe a few structures at least one of which will necessarily bepresent in any B1-EPG graph that does not admit a Helly representation. In addition, we show that the well known families of Blockgraphs, Cactus and Line of Bipartite graphs are totally contained inthe class Helly-B1-EPG.
publishDate 2021
dc.date.none.fl_str_mv 2021-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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://hdl.handle.net/11336/160294
Alcón, Liliana Graciela; Mazzoleni, María Pía; Dias Dos Santos, Tanilson; A note on Helly-B1-EPG graphs; Sociedad Brasilera de Matemàtica; Matemática Contemporânea; 48; 10-2021; 22-30
0103-9059
CONICET Digital
CONICET
url http://hdl.handle.net/11336/160294
identifier_str_mv Alcón, Liliana Graciela; Mazzoleni, María Pía; Dias Dos Santos, Tanilson; A note on Helly-B1-EPG graphs; Sociedad Brasilera de Matemàtica; Matemática Contemporânea; 48; 10-2021; 22-30
0103-9059
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.21711/231766362021/rmc483
info:eu-repo/semantics/altIdentifier/url/https://mc.sbm.org.br/wp-content/uploads/sites/9/sites/9/2022/01/Article-03-vol-48.pdf
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Sociedad Brasilera de Matemàtica
publisher.none.fl_str_mv Sociedad Brasilera de Matemàtica
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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