Characterizing paths graphs on bounded degree trees by minimal forbidden induced subgraphs

Autores
Alcón, Liliana Graciela; Gutierrez, Marisa; Mazzoleni, María Pía
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
An undirected graph G is called a VPT graph if it is the vertex intersection graph of a family of paths in a tree. The class of graphs which admit a VPT representation in a host tree with maximum degree at most h is denoted by [h,2,1]. The classes [h,2,1] are closed under taking induced subgraphs, therefore each one can be characterized by a family of minimal forbidden induced subgraphs. In this paper we associate the minimal forbidden induced subgraphs for [h,2,1] which are VPT with (color) h-critical graphs. We describe how to obtain minimal forbidden induced subgraphs from critical graphs, even more, we show that the family of graphs obtained using our procedure is exactly the family of VPT minimal forbidden induced subgraphs for [h,2,1]. The members of this family together with the minimal forbidden induced subgraphs for VPT (Lévêque et al., 2009; Tondato, 2009), are the minimal forbidden induced subgraphs for [h,2,1], with h ≥ 3. By taking h=3 we obtain a characterization by minimal forbidden induced subgraphs of the class V PT∩EPT=EPT∩Chordal=[3,2,2]=[3,2,1] (see Golumbic and Jamison, 1985).
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: 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
Materia
CRITICAL GRAPHS
FORBIDDEN SUBGRAPHS
INTERSECTION GRAPHS
REPRESENTATIONS ON TREES
VPT 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:11336/129995
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Characterizing paths graphs on bounded degree trees by minimal forbidden induced subgraphsAlcón, Liliana GracielaGutierrez, MarisaMazzoleni, María PíaCRITICAL GRAPHSFORBIDDEN SUBGRAPHSINTERSECTION GRAPHSREPRESENTATIONS ON TREESVPT GRAPHShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1An undirected graph G is called a VPT graph if it is the vertex intersection graph of a family of paths in a tree. The class of graphs which admit a VPT representation in a host tree with maximum degree at most h is denoted by [h,2,1]. The classes [h,2,1] are closed under taking induced subgraphs, therefore each one can be characterized by a family of minimal forbidden induced subgraphs. In this paper we associate the minimal forbidden induced subgraphs for [h,2,1] which are VPT with (color) h-critical graphs. We describe how to obtain minimal forbidden induced subgraphs from critical graphs, even more, we show that the family of graphs obtained using our procedure is exactly the family of VPT minimal forbidden induced subgraphs for [h,2,1]. The members of this family together with the minimal forbidden induced subgraphs for VPT (Lévêque et al., 2009; Tondato, 2009), are the minimal forbidden induced subgraphs for [h,2,1], with h ≥ 3. By taking h=3 we obtain a characterization by minimal forbidden induced subgraphs of the class V PT∩EPT=EPT∩Chordal=[3,2,2]=[3,2,1] (see Golumbic and Jamison, 1985).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: 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; ArgentinaElsevier Science2015-01info: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/11336/129995Alcón, Liliana Graciela; Gutierrez, Marisa; Mazzoleni, María Pía; Characterizing paths graphs on bounded degree trees by minimal forbidden induced subgraphs; Elsevier Science; Discrete Mathematics; 338; 1-2015; 103-1100012-365XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.disc.2014.08.020info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0012365X14003434?via%3Dihubinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:08:12Zoai:ri.conicet.gov.ar:11336/129995instacron: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 10:08:12.397CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Characterizing paths graphs on bounded degree trees by minimal forbidden induced subgraphs
title Characterizing paths graphs on bounded degree trees by minimal forbidden induced subgraphs
spellingShingle Characterizing paths graphs on bounded degree trees by minimal forbidden induced subgraphs
Alcón, Liliana Graciela
CRITICAL GRAPHS
FORBIDDEN SUBGRAPHS
INTERSECTION GRAPHS
REPRESENTATIONS ON TREES
VPT GRAPHS
title_short Characterizing paths graphs on bounded degree trees by minimal forbidden induced subgraphs
title_full Characterizing paths graphs on bounded degree trees by minimal forbidden induced subgraphs
title_fullStr Characterizing paths graphs on bounded degree trees by minimal forbidden induced subgraphs
title_full_unstemmed Characterizing paths graphs on bounded degree trees by minimal forbidden induced subgraphs
title_sort Characterizing paths graphs on bounded degree trees by minimal forbidden induced subgraphs
dc.creator.none.fl_str_mv Alcón, Liliana Graciela
Gutierrez, Marisa
Mazzoleni, María Pía
author Alcón, Liliana Graciela
author_facet Alcón, Liliana Graciela
Gutierrez, Marisa
Mazzoleni, María Pía
author_role author
author2 Gutierrez, Marisa
Mazzoleni, María Pía
author2_role author
author
dc.subject.none.fl_str_mv CRITICAL GRAPHS
FORBIDDEN SUBGRAPHS
INTERSECTION GRAPHS
REPRESENTATIONS ON TREES
VPT GRAPHS
topic CRITICAL GRAPHS
FORBIDDEN SUBGRAPHS
INTERSECTION GRAPHS
REPRESENTATIONS ON TREES
VPT 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 An undirected graph G is called a VPT graph if it is the vertex intersection graph of a family of paths in a tree. The class of graphs which admit a VPT representation in a host tree with maximum degree at most h is denoted by [h,2,1]. The classes [h,2,1] are closed under taking induced subgraphs, therefore each one can be characterized by a family of minimal forbidden induced subgraphs. In this paper we associate the minimal forbidden induced subgraphs for [h,2,1] which are VPT with (color) h-critical graphs. We describe how to obtain minimal forbidden induced subgraphs from critical graphs, even more, we show that the family of graphs obtained using our procedure is exactly the family of VPT minimal forbidden induced subgraphs for [h,2,1]. The members of this family together with the minimal forbidden induced subgraphs for VPT (Lévêque et al., 2009; Tondato, 2009), are the minimal forbidden induced subgraphs for [h,2,1], with h ≥ 3. By taking h=3 we obtain a characterization by minimal forbidden induced subgraphs of the class V PT∩EPT=EPT∩Chordal=[3,2,2]=[3,2,1] (see Golumbic and Jamison, 1985).
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: 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
description An undirected graph G is called a VPT graph if it is the vertex intersection graph of a family of paths in a tree. The class of graphs which admit a VPT representation in a host tree with maximum degree at most h is denoted by [h,2,1]. The classes [h,2,1] are closed under taking induced subgraphs, therefore each one can be characterized by a family of minimal forbidden induced subgraphs. In this paper we associate the minimal forbidden induced subgraphs for [h,2,1] which are VPT with (color) h-critical graphs. We describe how to obtain minimal forbidden induced subgraphs from critical graphs, even more, we show that the family of graphs obtained using our procedure is exactly the family of VPT minimal forbidden induced subgraphs for [h,2,1]. The members of this family together with the minimal forbidden induced subgraphs for VPT (Lévêque et al., 2009; Tondato, 2009), are the minimal forbidden induced subgraphs for [h,2,1], with h ≥ 3. By taking h=3 we obtain a characterization by minimal forbidden induced subgraphs of the class V PT∩EPT=EPT∩Chordal=[3,2,2]=[3,2,1] (see Golumbic and Jamison, 1985).
publishDate 2015
dc.date.none.fl_str_mv 2015-01
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/11336/129995
Alcón, Liliana Graciela; Gutierrez, Marisa; Mazzoleni, María Pía; Characterizing paths graphs on bounded degree trees by minimal forbidden induced subgraphs; Elsevier Science; Discrete Mathematics; 338; 1-2015; 103-110
0012-365X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/129995
identifier_str_mv Alcón, Liliana Graciela; Gutierrez, Marisa; Mazzoleni, María Pía; Characterizing paths graphs on bounded degree trees by minimal forbidden induced subgraphs; Elsevier Science; Discrete Mathematics; 338; 1-2015; 103-110
0012-365X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.disc.2014.08.020
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0012365X14003434?via%3Dihub
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
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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