On nested and 2-nested graphs: Two subclasses of graphs between threshold and split graphs

Autores
Pardal, Nina; Duran, Guillermo Alfredo; Grippo, Luciano Norberto; Safe, Martin Dario
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A (0, 1)-matrix has the Consecutive Ones Property (C1P) for the rows if there is a permutation of its columns such that the ones in each row appear consecutively. We say a (0, 1)-matrix is nested if it has the consecutive ones property for the rows (C1P) and every two rows are either disjoint or nested. We say a (0, 1)-matrix is 2-nested if it has the C1P and admits a partition of its rows into two sets such that the submatrix induced by each of these sets is nested. We say a split graph G with split partition (K, S) is nested (resp. 2-nested) if the matrix A(S, K) which indicates the adjacency between vertices in S and K is nested (resp. 2-nested). In this work, we characterize nested and 2-nested matrices by minimal forbidden submatrices. This characterization leads to a minimal forbidden induced subgraph characterization of these graph classes, which are superclasses of threshold graphs and subclasses of split and circle graphs.
Fil: Pardal, Nina. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Duran, Guillermo Alfredo. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Safe, Martin Dario. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Split Graphs
Threshold Graphs
Circle Graphs
Intersection Graphs
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:11336/147432

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spelling On nested and 2-nested graphs: Two subclasses of graphs between threshold and split graphsPardal, NinaDuran, Guillermo AlfredoGrippo, Luciano NorbertoSafe, Martin DarioSplit GraphsThreshold GraphsCircle GraphsIntersection Graphshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A (0, 1)-matrix has the Consecutive Ones Property (C1P) for the rows if there is a permutation of its columns such that the ones in each row appear consecutively. We say a (0, 1)-matrix is nested if it has the consecutive ones property for the rows (C1P) and every two rows are either disjoint or nested. We say a (0, 1)-matrix is 2-nested if it has the C1P and admits a partition of its rows into two sets such that the submatrix induced by each of these sets is nested. We say a split graph G with split partition (K, S) is nested (resp. 2-nested) if the matrix A(S, K) which indicates the adjacency between vertices in S and K is nested (resp. 2-nested). In this work, we characterize nested and 2-nested matrices by minimal forbidden submatrices. This characterization leads to a minimal forbidden induced subgraph characterization of these graph classes, which are superclasses of threshold graphs and subclasses of split and circle graphs.Fil: Pardal, Nina. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Duran, Guillermo Alfredo. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Safe, Martin Dario. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaSociedade Brasileira de Matematica2019-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/147432Pardal, Nina; Duran, Guillermo Alfredo; Grippo, Luciano Norberto; Safe, Martin Dario; On nested and 2-nested graphs: Two subclasses of graphs between threshold and split graphs; Sociedade Brasileira de Matematica; Matemática Contemporânea; 46; 6-2019; 119-1280103-9059CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1906.11970info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:24:19Zoai:ri.conicet.gov.ar:11336/147432instacron: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:34982025-10-15 14:24:19.985CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On nested and 2-nested graphs: Two subclasses of graphs between threshold and split graphs
title On nested and 2-nested graphs: Two subclasses of graphs between threshold and split graphs
spellingShingle On nested and 2-nested graphs: Two subclasses of graphs between threshold and split graphs
Pardal, Nina
Split Graphs
Threshold Graphs
Circle Graphs
Intersection Graphs
title_short On nested and 2-nested graphs: Two subclasses of graphs between threshold and split graphs
title_full On nested and 2-nested graphs: Two subclasses of graphs between threshold and split graphs
title_fullStr On nested and 2-nested graphs: Two subclasses of graphs between threshold and split graphs
title_full_unstemmed On nested and 2-nested graphs: Two subclasses of graphs between threshold and split graphs
title_sort On nested and 2-nested graphs: Two subclasses of graphs between threshold and split graphs
dc.creator.none.fl_str_mv Pardal, Nina
Duran, Guillermo Alfredo
Grippo, Luciano Norberto
Safe, Martin Dario
author Pardal, Nina
author_facet Pardal, Nina
Duran, Guillermo Alfredo
Grippo, Luciano Norberto
Safe, Martin Dario
author_role author
author2 Duran, Guillermo Alfredo
Grippo, Luciano Norberto
Safe, Martin Dario
author2_role author
author
author
dc.subject.none.fl_str_mv Split Graphs
Threshold Graphs
Circle Graphs
Intersection Graphs
topic Split Graphs
Threshold Graphs
Circle Graphs
Intersection Graphs
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv A (0, 1)-matrix has the Consecutive Ones Property (C1P) for the rows if there is a permutation of its columns such that the ones in each row appear consecutively. We say a (0, 1)-matrix is nested if it has the consecutive ones property for the rows (C1P) and every two rows are either disjoint or nested. We say a (0, 1)-matrix is 2-nested if it has the C1P and admits a partition of its rows into two sets such that the submatrix induced by each of these sets is nested. We say a split graph G with split partition (K, S) is nested (resp. 2-nested) if the matrix A(S, K) which indicates the adjacency between vertices in S and K is nested (resp. 2-nested). In this work, we characterize nested and 2-nested matrices by minimal forbidden submatrices. This characterization leads to a minimal forbidden induced subgraph characterization of these graph classes, which are superclasses of threshold graphs and subclasses of split and circle graphs.
Fil: Pardal, Nina. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Duran, Guillermo Alfredo. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Safe, Martin Dario. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description A (0, 1)-matrix has the Consecutive Ones Property (C1P) for the rows if there is a permutation of its columns such that the ones in each row appear consecutively. We say a (0, 1)-matrix is nested if it has the consecutive ones property for the rows (C1P) and every two rows are either disjoint or nested. We say a (0, 1)-matrix is 2-nested if it has the C1P and admits a partition of its rows into two sets such that the submatrix induced by each of these sets is nested. We say a split graph G with split partition (K, S) is nested (resp. 2-nested) if the matrix A(S, K) which indicates the adjacency between vertices in S and K is nested (resp. 2-nested). In this work, we characterize nested and 2-nested matrices by minimal forbidden submatrices. This characterization leads to a minimal forbidden induced subgraph characterization of these graph classes, which are superclasses of threshold graphs and subclasses of split and circle graphs.
publishDate 2019
dc.date.none.fl_str_mv 2019-06
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/11336/147432
Pardal, Nina; Duran, Guillermo Alfredo; Grippo, Luciano Norberto; Safe, Martin Dario; On nested and 2-nested graphs: Two subclasses of graphs between threshold and split graphs; Sociedade Brasileira de Matematica; Matemática Contemporânea; 46; 6-2019; 119-128
0103-9059
CONICET Digital
CONICET
url http://hdl.handle.net/11336/147432
identifier_str_mv Pardal, Nina; Duran, Guillermo Alfredo; Grippo, Luciano Norberto; Safe, Martin Dario; On nested and 2-nested graphs: Two subclasses of graphs between threshold and split graphs; Sociedade Brasileira de Matematica; Matemática Contemporânea; 46; 6-2019; 119-128
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/url/https://arxiv.org/abs/1906.11970
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
application/pdf
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matematica
publisher.none.fl_str_mv Sociedade Brasileira de Matematica
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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