Thinness and its variations on some graph families and coloring graphs of bounded thinness

Autores
Bonomo, Flavia; Brandwein, Eric; Oliveira, Fabiano S.; Sampaio, Moysés S.; Sansone, Agustín; Szwarcfiter, Jayme L.
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Interval graphs and proper interval graphs are well known graph classes, for which several generalizations have been proposed in the literature. In this work, we study the (proper) thinness, and several variations, for the classes of cographs, crowns graphs and grid graphs.We provide the exact values for several variants of thinness (proper, independent, complete, precedence, and combinations of them) for the crown graphs $CR_n$. For cographs, we prove that the precedence thinness can be determined in polynomial time. We also improve known bounds for the thinness of $n imes n$ grids $GR_n$ and $m imes n$ grids $GR_{m,n}$, proving that $left lceil rac{n-1}{3} ight ceil leq thin(GR_n) leq left lceil rac{n+1}{2} ight ceil$. Regarding the precedence thinness, we prove that $prec-thin(GR_{n,2}) = left lceil rac{n+1}{2} ight ceil$ and that $left lceil rac{n-1}{3} ight ceil left lceilrac{n-1}{2} ight ceil + 1 leq prec-thin(GR_n) leq left lceilrac{n-1}{2} ight ceil^2+1$. As applications, we show that the $k$-coloring problem is NP-complete for precedence $2$-thin graphs and for proper $2$-thin graphs, when $k$ is part of the input. On the positive side, it is polynomially solvable for precedence proper $2$-thin graphs, given the order and partition.
Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina
Fil: Brandwein, Eric. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Fil: Oliveira, Fabiano S.. Universidade do Estado de Rio do Janeiro; Brasil
Fil: Sampaio, Moysés S.. Universidade Federal do Rio de Janeiro; Brasil
Fil: Sansone, Agustín. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Fil: Szwarcfiter, Jayme L.. Universidade do Estado de Rio do Janeiro; Brasil. Universidade Federal do Rio de Janeiro; Brasil
Materia
(proper) k-thin graphs
cographs
crown graphs
grid graphs
graph coloring
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:11336/258769
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Thinness and its variations on some graph families and coloring graphs of bounded thinnessBonomo, FlaviaBrandwein, EricOliveira, Fabiano S.Sampaio, Moysés S.Sansone, AgustínSzwarcfiter, Jayme L.(proper) k-thin graphscographscrown graphsgrid graphsgraph coloringhttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Interval graphs and proper interval graphs are well known graph classes, for which several generalizations have been proposed in the literature. In this work, we study the (proper) thinness, and several variations, for the classes of cographs, crowns graphs and grid graphs.We provide the exact values for several variants of thinness (proper, independent, complete, precedence, and combinations of them) for the crown graphs $CR_n$. For cographs, we prove that the precedence thinness can be determined in polynomial time. We also improve known bounds for the thinness of $n imes n$ grids $GR_n$ and $m imes n$ grids $GR_{m,n}$, proving that $left lceil rac{n-1}{3} ight ceil leq thin(GR_n) leq left lceil rac{n+1}{2} ight ceil$. Regarding the precedence thinness, we prove that $prec-thin(GR_{n,2}) = left lceil rac{n+1}{2} ight ceil$ and that $left lceil rac{n-1}{3} ight ceil left lceilrac{n-1}{2} ight ceil + 1 leq prec-thin(GR_n) leq left lceilrac{n-1}{2} ight ceil^2+1$. As applications, we show that the $k$-coloring problem is NP-complete for precedence $2$-thin graphs and for proper $2$-thin graphs, when $k$ is part of the input. On the positive side, it is polynomially solvable for precedence proper $2$-thin graphs, given the order and partition.Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Brandwein, Eric. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Oliveira, Fabiano S.. Universidade do Estado de Rio do Janeiro; BrasilFil: Sampaio, Moysés S.. Universidade Federal do Rio de Janeiro; BrasilFil: Sansone, Agustín. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Szwarcfiter, Jayme L.. Universidade do Estado de Rio do Janeiro; Brasil. Universidade Federal do Rio de Janeiro; BrasilEDP Sciences2024-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/258769Bonomo, Flavia; Brandwein, Eric; Oliveira, Fabiano S.; Sampaio, Moysés S.; Sansone, Agustín; et al.; Thinness and its variations on some graph families and coloring graphs of bounded thinness; EDP Sciences; Rairo - Recherche Operationnelle (operations Research); 58; 2; 4-2024; 1681-17020399-0559CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1051/ro/2024033info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:48:50Zoai:ri.conicet.gov.ar:11336/258769instacron: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 09:48:50.428CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Thinness and its variations on some graph families and coloring graphs of bounded thinness
title Thinness and its variations on some graph families and coloring graphs of bounded thinness
spellingShingle Thinness and its variations on some graph families and coloring graphs of bounded thinness
Bonomo, Flavia
(proper) k-thin graphs
cographs
crown graphs
grid graphs
graph coloring
title_short Thinness and its variations on some graph families and coloring graphs of bounded thinness
title_full Thinness and its variations on some graph families and coloring graphs of bounded thinness
title_fullStr Thinness and its variations on some graph families and coloring graphs of bounded thinness
title_full_unstemmed Thinness and its variations on some graph families and coloring graphs of bounded thinness
title_sort Thinness and its variations on some graph families and coloring graphs of bounded thinness
dc.creator.none.fl_str_mv Bonomo, Flavia
Brandwein, Eric
Oliveira, Fabiano S.
Sampaio, Moysés S.
Sansone, Agustín
Szwarcfiter, Jayme L.
author Bonomo, Flavia
author_facet Bonomo, Flavia
Brandwein, Eric
Oliveira, Fabiano S.
Sampaio, Moysés S.
Sansone, Agustín
Szwarcfiter, Jayme L.
author_role author
author2 Brandwein, Eric
Oliveira, Fabiano S.
Sampaio, Moysés S.
Sansone, Agustín
Szwarcfiter, Jayme L.
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv (proper) k-thin graphs
cographs
crown graphs
grid graphs
graph coloring
topic (proper) k-thin graphs
cographs
crown graphs
grid graphs
graph coloring
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Interval graphs and proper interval graphs are well known graph classes, for which several generalizations have been proposed in the literature. In this work, we study the (proper) thinness, and several variations, for the classes of cographs, crowns graphs and grid graphs.We provide the exact values for several variants of thinness (proper, independent, complete, precedence, and combinations of them) for the crown graphs $CR_n$. For cographs, we prove that the precedence thinness can be determined in polynomial time. We also improve known bounds for the thinness of $n imes n$ grids $GR_n$ and $m imes n$ grids $GR_{m,n}$, proving that $left lceil rac{n-1}{3} ight ceil leq thin(GR_n) leq left lceil rac{n+1}{2} ight ceil$. Regarding the precedence thinness, we prove that $prec-thin(GR_{n,2}) = left lceil rac{n+1}{2} ight ceil$ and that $left lceil rac{n-1}{3} ight ceil left lceilrac{n-1}{2} ight ceil + 1 leq prec-thin(GR_n) leq left lceilrac{n-1}{2} ight ceil^2+1$. As applications, we show that the $k$-coloring problem is NP-complete for precedence $2$-thin graphs and for proper $2$-thin graphs, when $k$ is part of the input. On the positive side, it is polynomially solvable for precedence proper $2$-thin graphs, given the order and partition.
Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina
Fil: Brandwein, Eric. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Fil: Oliveira, Fabiano S.. Universidade do Estado de Rio do Janeiro; Brasil
Fil: Sampaio, Moysés S.. Universidade Federal do Rio de Janeiro; Brasil
Fil: Sansone, Agustín. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Fil: Szwarcfiter, Jayme L.. Universidade do Estado de Rio do Janeiro; Brasil. Universidade Federal do Rio de Janeiro; Brasil
description Interval graphs and proper interval graphs are well known graph classes, for which several generalizations have been proposed in the literature. In this work, we study the (proper) thinness, and several variations, for the classes of cographs, crowns graphs and grid graphs.We provide the exact values for several variants of thinness (proper, independent, complete, precedence, and combinations of them) for the crown graphs $CR_n$. For cographs, we prove that the precedence thinness can be determined in polynomial time. We also improve known bounds for the thinness of $n imes n$ grids $GR_n$ and $m imes n$ grids $GR_{m,n}$, proving that $left lceil rac{n-1}{3} ight ceil leq thin(GR_n) leq left lceil rac{n+1}{2} ight ceil$. Regarding the precedence thinness, we prove that $prec-thin(GR_{n,2}) = left lceil rac{n+1}{2} ight ceil$ and that $left lceil rac{n-1}{3} ight ceil left lceilrac{n-1}{2} ight ceil + 1 leq prec-thin(GR_n) leq left lceilrac{n-1}{2} ight ceil^2+1$. As applications, we show that the $k$-coloring problem is NP-complete for precedence $2$-thin graphs and for proper $2$-thin graphs, when $k$ is part of the input. On the positive side, it is polynomially solvable for precedence proper $2$-thin graphs, given the order and partition.
publishDate 2024
dc.date.none.fl_str_mv 2024-04
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/11336/258769
Bonomo, Flavia; Brandwein, Eric; Oliveira, Fabiano S.; Sampaio, Moysés S.; Sansone, Agustín; et al.; Thinness and its variations on some graph families and coloring graphs of bounded thinness; EDP Sciences; Rairo - Recherche Operationnelle (operations Research); 58; 2; 4-2024; 1681-1702
0399-0559
CONICET Digital
CONICET
url http://hdl.handle.net/11336/258769
identifier_str_mv Bonomo, Flavia; Brandwein, Eric; Oliveira, Fabiano S.; Sampaio, Moysés S.; Sansone, Agustín; et al.; Thinness and its variations on some graph families and coloring graphs of bounded thinness; EDP Sciences; Rairo - Recherche Operationnelle (operations Research); 58; 2; 4-2024; 1681-1702
0399-0559
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1051/ro/2024033
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 EDP Sciences
publisher.none.fl_str_mv EDP Sciences
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 13.070432

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