The star and biclique coloring and choosability problems

Autores
Groshaus, Marina Esther; Soulignac, Francisco Juan; Terlisky, Pablo Ezequiel
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A biclique of a graph G is an induced complete bipartite graph. A star of G is a biclique contained in the closed neighborhood of a vertex. A star (biclique) k-coloring of G is a k-coloring of G that contains no monochromatic maximal stars (bicliques). Similarly, for a list assignment L of G, a star (biclique) L-coloring is an L-coloring of G in which no maximal star (biclique) is monochromatic. If G admits a star (biclique) L- coloring for every k-list assignment L, then G is said to be star (biclique) k-choosable. In this article we study the computational complexity of the star and biclique coloring and choosability problems. Specifically, we prove that the star (biclique) k-coloring and k-choosability problems are Σp2-complete and IIp3-complete for k > 2, respectively, even when the input graph contains no induced C4 or Kk+2. Then, we study all these problems in some related classes of graphs, including H-free graphs for every H on three vertices, graphs with restricted diamonds, split graphs, and threshold graphs.
Fil: Groshaus, Marina Esther. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Soulignac, Francisco Juan. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Terlisky, Pablo Ezequiel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Biclique
Coloring
Choosability Problems
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/84531
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The star and biclique coloring and choosability problemsGroshaus, Marina EstherSoulignac, Francisco JuanTerlisky, Pablo EzequielBicliqueColoringChoosability Problemshttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A biclique of a graph G is an induced complete bipartite graph. A star of G is a biclique contained in the closed neighborhood of a vertex. A star (biclique) k-coloring of G is a k-coloring of G that contains no monochromatic maximal stars (bicliques). Similarly, for a list assignment L of G, a star (biclique) L-coloring is an L-coloring of G in which no maximal star (biclique) is monochromatic. If G admits a star (biclique) L- coloring for every k-list assignment L, then G is said to be star (biclique) k-choosable. In this article we study the computational complexity of the star and biclique coloring and choosability problems. Specifically, we prove that the star (biclique) k-coloring and k-choosability problems are Σp2-complete and IIp3-complete for k > 2, respectively, even when the input graph contains no induced C4 or Kk+2. Then, we study all these problems in some related classes of graphs, including H-free graphs for every H on three vertices, graphs with restricted diamonds, split graphs, and threshold graphs.Fil: Groshaus, Marina Esther. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Soulignac, Francisco Juan. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Terlisky, Pablo Ezequiel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaBrown University2014-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/84531Groshaus, Marina Esther; Soulignac, Francisco Juan; Terlisky, Pablo Ezequiel; The star and biclique coloring and choosability problems; Brown University; Journal of Graph Algorithms and Applications; 18; 3; 5-2014; 347-3831526-1719CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://jgaa.info/accepted/2014/GroshausSoulignacTerlisky2014.18.3.pdfinfo:eu-repo/semantics/altIdentifier/doi/10.7155/jgaa.00326info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:08:44Zoai:ri.conicet.gov.ar:11336/84531instacron: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:34982025-10-22 12:08:44.292CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The star and biclique coloring and choosability problems
title The star and biclique coloring and choosability problems
spellingShingle The star and biclique coloring and choosability problems
Groshaus, Marina Esther
Biclique
Coloring
Choosability Problems
title_short The star and biclique coloring and choosability problems
title_full The star and biclique coloring and choosability problems
title_fullStr The star and biclique coloring and choosability problems
title_full_unstemmed The star and biclique coloring and choosability problems
title_sort The star and biclique coloring and choosability problems
dc.creator.none.fl_str_mv Groshaus, Marina Esther
Soulignac, Francisco Juan
Terlisky, Pablo Ezequiel
author Groshaus, Marina Esther
author_facet Groshaus, Marina Esther
Soulignac, Francisco Juan
Terlisky, Pablo Ezequiel
author_role author
author2 Soulignac, Francisco Juan
Terlisky, Pablo Ezequiel
author2_role author
author
dc.subject.none.fl_str_mv Biclique
Coloring
Choosability Problems
topic Biclique
Coloring
Choosability Problems
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 A biclique of a graph G is an induced complete bipartite graph. A star of G is a biclique contained in the closed neighborhood of a vertex. A star (biclique) k-coloring of G is a k-coloring of G that contains no monochromatic maximal stars (bicliques). Similarly, for a list assignment L of G, a star (biclique) L-coloring is an L-coloring of G in which no maximal star (biclique) is monochromatic. If G admits a star (biclique) L- coloring for every k-list assignment L, then G is said to be star (biclique) k-choosable. In this article we study the computational complexity of the star and biclique coloring and choosability problems. Specifically, we prove that the star (biclique) k-coloring and k-choosability problems are Σp2-complete and IIp3-complete for k > 2, respectively, even when the input graph contains no induced C4 or Kk+2. Then, we study all these problems in some related classes of graphs, including H-free graphs for every H on three vertices, graphs with restricted diamonds, split graphs, and threshold graphs.
Fil: Groshaus, Marina Esther. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Soulignac, Francisco Juan. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Terlisky, Pablo Ezequiel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description A biclique of a graph G is an induced complete bipartite graph. A star of G is a biclique contained in the closed neighborhood of a vertex. A star (biclique) k-coloring of G is a k-coloring of G that contains no monochromatic maximal stars (bicliques). Similarly, for a list assignment L of G, a star (biclique) L-coloring is an L-coloring of G in which no maximal star (biclique) is monochromatic. If G admits a star (biclique) L- coloring for every k-list assignment L, then G is said to be star (biclique) k-choosable. In this article we study the computational complexity of the star and biclique coloring and choosability problems. Specifically, we prove that the star (biclique) k-coloring and k-choosability problems are Σp2-complete and IIp3-complete for k > 2, respectively, even when the input graph contains no induced C4 or Kk+2. Then, we study all these problems in some related classes of graphs, including H-free graphs for every H on three vertices, graphs with restricted diamonds, split graphs, and threshold graphs.
publishDate 2014
dc.date.none.fl_str_mv 2014-05
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/11336/84531
Groshaus, Marina Esther; Soulignac, Francisco Juan; Terlisky, Pablo Ezequiel; The star and biclique coloring and choosability problems; Brown University; Journal of Graph Algorithms and Applications; 18; 3; 5-2014; 347-383
1526-1719
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84531
identifier_str_mv Groshaus, Marina Esther; Soulignac, Francisco Juan; Terlisky, Pablo Ezequiel; The star and biclique coloring and choosability problems; Brown University; Journal of Graph Algorithms and Applications; 18; 3; 5-2014; 347-383
1526-1719
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://jgaa.info/accepted/2014/GroshausSoulignacTerlisky2014.18.3.pdf
info:eu-repo/semantics/altIdentifier/doi/10.7155/jgaa.00326
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Brown University
publisher.none.fl_str_mv Brown University
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 12.982451

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