Gromov hyperbolicity in strong product graphs

If X is a geodesic metric space and x1; x2; x3 2 X, a geodesic triangle T = fx1; x2; x3g is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is -hyperbolic (in the Gromov sense) if any side of T is contained in a -neighborhood of the union of the two other sides, for ever...

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Autores: Carballosa, Walter, Moreno Casablanca, Rocío, Cruz, Amauris de la, Rodríguez, José M.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2013
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/69450
Acceso en línea:https://hdl.handle.net/11441/69450
Access Level:acceso abierto
Palabra clave:Strong Product Graphs
Geodesics
Gromov Hyperbolicity
Infinite Graphs
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spelling Gromov hyperbolicity in strong product graphsCarballosa, WalterMoreno Casablanca, RocíoCruz, Amauris de laRodríguez, José M.Strong Product GraphsGeodesicsGromov HyperbolicityInfinite GraphsIf X is a geodesic metric space and x1; x2; x3 2 X, a geodesic triangle T = fx1; x2; x3g is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is -hyperbolic (in the Gromov sense) if any side of T is contained in a -neighborhood of the union of the two other sides, for every geodesic triangle T in X. If X is hyperbolic, we denote by (X) the sharp hyperbolicity constant of X, i.e. (X) = inff > 0 : X is -hyperbolic g : In this paper we characterize the strong product of two graphs G1 G2 which are hyperbolic, in terms of G1 and G2: the strong product graph G1 G2 is hyperbolic if and only if one of the factors is hyperbolic and the other one is bounded. We also prove some sharp relations between (G1 G2), (G1), (G2) and the diameters of G1 and G2 (and we nd families of graphs for which the inequalities are attained). Furthermore, we obtain the exact values of the hyperbolicity constant for many strong product graphs.E-JCMatemática Aplicada I2013info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/69450reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésElectronic Journal of Combinatorics, 20 (3)http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i3p2info:eu-repo/semantics/openAccessoai:idus.us.es:11441/694502026-06-17T12:51:07Z
dc.title.none.fl_str_mv Gromov hyperbolicity in strong product graphs
title Gromov hyperbolicity in strong product graphs
spellingShingle Gromov hyperbolicity in strong product graphs
Carballosa, Walter
Strong Product Graphs
Geodesics
Gromov Hyperbolicity
Infinite Graphs
title_short Gromov hyperbolicity in strong product graphs
title_full Gromov hyperbolicity in strong product graphs
title_fullStr Gromov hyperbolicity in strong product graphs
title_full_unstemmed Gromov hyperbolicity in strong product graphs
title_sort Gromov hyperbolicity in strong product graphs
dc.creator.none.fl_str_mv Carballosa, Walter
Moreno Casablanca, Rocío
Cruz, Amauris de la
Rodríguez, José M.
author Carballosa, Walter
author_facet Carballosa, Walter
Moreno Casablanca, Rocío
Cruz, Amauris de la
Rodríguez, José M.
author_role author
author2 Moreno Casablanca, Rocío
Cruz, Amauris de la
Rodríguez, José M.
author2_role author
author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
dc.subject.none.fl_str_mv Strong Product Graphs
Geodesics
Gromov Hyperbolicity
Infinite Graphs
topic Strong Product Graphs
Geodesics
Gromov Hyperbolicity
Infinite Graphs
description If X is a geodesic metric space and x1; x2; x3 2 X, a geodesic triangle T = fx1; x2; x3g is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is -hyperbolic (in the Gromov sense) if any side of T is contained in a -neighborhood of the union of the two other sides, for every geodesic triangle T in X. If X is hyperbolic, we denote by (X) the sharp hyperbolicity constant of X, i.e. (X) = inff > 0 : X is -hyperbolic g : In this paper we characterize the strong product of two graphs G1 G2 which are hyperbolic, in terms of G1 and G2: the strong product graph G1 G2 is hyperbolic if and only if one of the factors is hyperbolic and the other one is bounded. We also prove some sharp relations between (G1 G2), (G1), (G2) and the diameters of G1 and G2 (and we nd families of graphs for which the inequalities are attained). Furthermore, we obtain the exact values of the hyperbolicity constant for many strong product graphs.
publishDate 2013
dc.date.none.fl_str_mv 2013
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/69450
url https://hdl.handle.net/11441/69450
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Electronic Journal of Combinatorics, 20 (3)
http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i3p2
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv E-JC
publisher.none.fl_str_mv E-JC
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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