On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid

Autores
Alcón, Liliana Graciela; Bonomo, Flavia; Duran, Guillermo Alfredo; Gutierrez, Marisa; Mazzoleni, María Pía; Ries, Bernard; Valencia Pavón, Mario
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Golumbic, Lipshteyn and Stern [12] proved that every graph can be represented as the edge intersection graph of paths on a grid (EPG graph), i.e., one can associate with each vertex of the graph a nontrivial path on a rectangular grid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. For a nonnegative integer k, Bk-EPG graphs are defined as EPG graphs admitting a model in which each path has at most k bends. Circular-arc graphs are intersection graphs of open arcs of a circle. It is easy to see that every circular-arc graph is a B4-EPG graph, by embedding the circle into a rectangle of the grid. In this paper, we prove that circular-arc graphs are B3-EPG, and that there exist circular-arc graphs which are not B2-EPG. If we restrict ourselves to rectangular representations (i.e., the union of the paths used in the model is contained in the boundary of a rectangle of the grid), we obtain EPR (edge intersection of paths in a rectangle) representations. We may define Bk-EPR graphs, k≥0, the same way as Bk-EPG graphs. Circular-arc graphs are clearly B4-EPR graphs and we will show that there exist circular-arc graphs that are not B3-EPR graphs. We also show that normal circular-arc graphs are B2-EPR graphs and that there exist normal circular-arc graphs that are not B1-EPR graphs. Finally, we characterize B1-EPR graphs by a family of minimal forbidden induced subgraphs, and show that they form a subclass of normal Helly circular-arc graphs.
Fil: Alcón, Liliana Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Bonomo, Flavia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Cs.exactas y Naturales. Departamento de Computación. Algoritmos, Complejidad y Aplicaciones; Argentina
Fil: Duran, Guillermo Alfredo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Universidad de Chile; Chile
Fil: Gutierrez, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Mazzoleni, María Pía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Ries, Bernard. Université de Fribourg; Suiza
Fil: Valencia Pavón, Mario. Universite de Paris 13-Nord. Laboratoire d'informatique de L'Université Paris-Nord; Francia
Materia
(Normal, Helly) Circular-Arc Graphs
Edge Intersection Graphs
Forbidden Induced Subgraphs
Paths on A Grid
Powers of Cycles
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/83118
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/83118
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On the bend number of circular-arc graphs as edge intersection graphs of paths on a gridAlcón, Liliana GracielaBonomo, FlaviaDuran, Guillermo AlfredoGutierrez, MarisaMazzoleni, María PíaRies, BernardValencia Pavón, Mario(Normal, Helly) Circular-Arc GraphsEdge Intersection GraphsForbidden Induced SubgraphsPaths on A GridPowers of Cycleshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Golumbic, Lipshteyn and Stern [12] proved that every graph can be represented as the edge intersection graph of paths on a grid (EPG graph), i.e., one can associate with each vertex of the graph a nontrivial path on a rectangular grid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. For a nonnegative integer k, Bk-EPG graphs are defined as EPG graphs admitting a model in which each path has at most k bends. Circular-arc graphs are intersection graphs of open arcs of a circle. It is easy to see that every circular-arc graph is a B4-EPG graph, by embedding the circle into a rectangle of the grid. In this paper, we prove that circular-arc graphs are B3-EPG, and that there exist circular-arc graphs which are not B2-EPG. If we restrict ourselves to rectangular representations (i.e., the union of the paths used in the model is contained in the boundary of a rectangle of the grid), we obtain EPR (edge intersection of paths in a rectangle) representations. We may define Bk-EPR graphs, k≥0, the same way as Bk-EPG graphs. Circular-arc graphs are clearly B4-EPR graphs and we will show that there exist circular-arc graphs that are not B3-EPR graphs. We also show that normal circular-arc graphs are B2-EPR graphs and that there exist normal circular-arc graphs that are not B1-EPR graphs. Finally, we characterize B1-EPR graphs by a family of minimal forbidden induced subgraphs, and show that they form a subclass of normal Helly circular-arc graphs.Fil: Alcón, Liliana Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: Bonomo, Flavia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Cs.exactas y Naturales. Departamento de Computación. Algoritmos, Complejidad y Aplicaciones; ArgentinaFil: Duran, Guillermo Alfredo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Universidad de Chile; ChileFil: Gutierrez, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: Mazzoleni, María Pía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: Ries, Bernard. Université de Fribourg; SuizaFil: Valencia Pavón, Mario. Universite de Paris 13-Nord. Laboratoire d'informatique de L'Université Paris-Nord; FranciaElsevier Science2018-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/83118Alcón, Liliana Graciela; Bonomo, Flavia; Duran, Guillermo Alfredo; Gutierrez, Marisa; Mazzoleni, María Pía; et al.; On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid; Elsevier Science; Discrete Applied Mathematics; 234; 1-2018; 12-210166-218XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0166218X16303687info:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2016.08.004info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1506.08750info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:03:46Zoai:ri.conicet.gov.ar:11336/83118instacron: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 10:03:46.446CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
title On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
spellingShingle On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
Alcón, Liliana Graciela
(Normal, Helly) Circular-Arc Graphs
Edge Intersection Graphs
Forbidden Induced Subgraphs
Paths on A Grid
Powers of Cycles
title_short On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
title_full On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
title_fullStr On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
title_full_unstemmed On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
title_sort On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
dc.creator.none.fl_str_mv Alcón, Liliana Graciela
Bonomo, Flavia
Duran, Guillermo Alfredo
Gutierrez, Marisa
Mazzoleni, María Pía
Ries, Bernard
Valencia Pavón, Mario
author Alcón, Liliana Graciela
author_facet Alcón, Liliana Graciela
Bonomo, Flavia
Duran, Guillermo Alfredo
Gutierrez, Marisa
Mazzoleni, María Pía
Ries, Bernard
Valencia Pavón, Mario
author_role author
author2 Bonomo, Flavia
Duran, Guillermo Alfredo
Gutierrez, Marisa
Mazzoleni, María Pía
Ries, Bernard
Valencia Pavón, Mario
author2_role author
author
author
author
author
author
dc.subject.none.fl_str_mv (Normal, Helly) Circular-Arc Graphs
Edge Intersection Graphs
Forbidden Induced Subgraphs
Paths on A Grid
Powers of Cycles
topic (Normal, Helly) Circular-Arc Graphs
Edge Intersection Graphs
Forbidden Induced Subgraphs
Paths on A Grid
Powers of Cycles
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Golumbic, Lipshteyn and Stern [12] proved that every graph can be represented as the edge intersection graph of paths on a grid (EPG graph), i.e., one can associate with each vertex of the graph a nontrivial path on a rectangular grid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. For a nonnegative integer k, Bk-EPG graphs are defined as EPG graphs admitting a model in which each path has at most k bends. Circular-arc graphs are intersection graphs of open arcs of a circle. It is easy to see that every circular-arc graph is a B4-EPG graph, by embedding the circle into a rectangle of the grid. In this paper, we prove that circular-arc graphs are B3-EPG, and that there exist circular-arc graphs which are not B2-EPG. If we restrict ourselves to rectangular representations (i.e., the union of the paths used in the model is contained in the boundary of a rectangle of the grid), we obtain EPR (edge intersection of paths in a rectangle) representations. We may define Bk-EPR graphs, k≥0, the same way as Bk-EPG graphs. Circular-arc graphs are clearly B4-EPR graphs and we will show that there exist circular-arc graphs that are not B3-EPR graphs. We also show that normal circular-arc graphs are B2-EPR graphs and that there exist normal circular-arc graphs that are not B1-EPR graphs. Finally, we characterize B1-EPR graphs by a family of minimal forbidden induced subgraphs, and show that they form a subclass of normal Helly circular-arc graphs.
Fil: Alcón, Liliana Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Bonomo, Flavia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Cs.exactas y Naturales. Departamento de Computación. Algoritmos, Complejidad y Aplicaciones; Argentina
Fil: Duran, Guillermo Alfredo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Universidad de Chile; Chile
Fil: Gutierrez, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Mazzoleni, María Pía. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Ries, Bernard. Université de Fribourg; Suiza
Fil: Valencia Pavón, Mario. Universite de Paris 13-Nord. Laboratoire d'informatique de L'Université Paris-Nord; Francia
description Golumbic, Lipshteyn and Stern [12] proved that every graph can be represented as the edge intersection graph of paths on a grid (EPG graph), i.e., one can associate with each vertex of the graph a nontrivial path on a rectangular grid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. For a nonnegative integer k, Bk-EPG graphs are defined as EPG graphs admitting a model in which each path has at most k bends. Circular-arc graphs are intersection graphs of open arcs of a circle. It is easy to see that every circular-arc graph is a B4-EPG graph, by embedding the circle into a rectangle of the grid. In this paper, we prove that circular-arc graphs are B3-EPG, and that there exist circular-arc graphs which are not B2-EPG. If we restrict ourselves to rectangular representations (i.e., the union of the paths used in the model is contained in the boundary of a rectangle of the grid), we obtain EPR (edge intersection of paths in a rectangle) representations. We may define Bk-EPR graphs, k≥0, the same way as Bk-EPG graphs. Circular-arc graphs are clearly B4-EPR graphs and we will show that there exist circular-arc graphs that are not B3-EPR graphs. We also show that normal circular-arc graphs are B2-EPR graphs and that there exist normal circular-arc graphs that are not B1-EPR graphs. Finally, we characterize B1-EPR graphs by a family of minimal forbidden induced subgraphs, and show that they form a subclass of normal Helly circular-arc graphs.
publishDate 2018
dc.date.none.fl_str_mv 2018-01
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/11336/83118
Alcón, Liliana Graciela; Bonomo, Flavia; Duran, Guillermo Alfredo; Gutierrez, Marisa; Mazzoleni, María Pía; et al.; On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid; Elsevier Science; Discrete Applied Mathematics; 234; 1-2018; 12-21
0166-218X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/83118
identifier_str_mv Alcón, Liliana Graciela; Bonomo, Flavia; Duran, Guillermo Alfredo; Gutierrez, Marisa; Mazzoleni, María Pía; et al.; On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid; Elsevier Science; Discrete Applied Mathematics; 234; 1-2018; 12-21
0166-218X
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/S0166218X16303687
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2016.08.004
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1506.08750
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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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score 13.13397

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