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

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, t...

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Autores: Alcón, Liliana Graciela, Gutiérrez, Marisa, Mazzoleni, María Pía
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2015
País:Argentina
Institución:Universidad Nacional de La Plata
Repositorio:SEDICI (UNLP)
Idioma:inglés
OAI Identifier:oai:sedici.unlp.edu.ar:10915/85830
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/85830
Access Level:acceso abierto
Palabra clave:Matemática
Critical graphs
Forbidden subgraphs
Intersection graphs
Representations on trees
VPT graphs
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spelling Characterizing paths graphs on bounded degree trees by minimal forbidden induced subgraphsAlcón, Liliana GracielaGutiérrez, MarisaMazzoleni, María PíaMatemáticaCritical graphsForbidden subgraphsIntersection graphsRepresentations on treesVPT graphsAn 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).Facultad de Ciencias Exactas2015info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf103-110http://sedici.unlp.edu.ar/handle/10915/85830enginfo:eu-repo/semantics/altIdentifier/issn/0012-365Xinfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.disc.2014.08.020info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2024-05-08T12:54:51Zoai:sedici.unlp.edu.ar:10915/85830Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292024-05-08 12:54:51.329SEDICI (UNLP) - Universidad Nacional de La Platafalse
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
Matemática
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
Gutiérrez, Marisa
Mazzoleni, María Pía
author Alcón, Liliana Graciela
author_facet Alcón, Liliana Graciela
Gutiérrez, Marisa
Mazzoleni, María Pía
author_role author
author2 Gutiérrez, Marisa
Mazzoleni, María Pía
author2_role author
author
dc.subject.none.fl_str_mv Matemática
Critical graphs
Forbidden subgraphs
Intersection graphs
Representations on trees
VPT graphs
topic Matemática
Critical graphs
Forbidden subgraphs
Intersection graphs
Representations on trees
VPT graphs
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
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/85830
url http://sedici.unlp.edu.ar/handle/10915/85830
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0012-365X
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.disc.2014.08.020
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
103-110
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
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instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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