Separating the Edges of a Graph by Cycles and by Subdivisions of K4

A separating system of a graph (Formula presented.) is a family (Formula presented.) of subgraphs of (Formula presented.) for which the following holds: for all distinct edges (Formula presented.) and (Formula presented.) of (Formula presented.), there exists an element in (Formula presented.) that...

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Detalles Bibliográficos
Autores: Botler, F., Naia, Tássio
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/484458
Acceso en línea:http://hdl.handle.net/2072/484458
Access Level:acceso abierto
Palabra clave:Graph
Separating system
Subdivision
51
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spelling Separating the Edges of a Graph by Cycles and by Subdivisions of K4Botler, F.Naia, TássioGraphSeparating systemSubdivision51A separating system of a graph (Formula presented.) is a family (Formula presented.) of subgraphs of (Formula presented.) for which the following holds: for all distinct edges (Formula presented.) and (Formula presented.) of (Formula presented.), there exists an element in (Formula presented.) that contains (Formula presented.) but not (Formula presented.). Recently, it has been shown that every graph of order (Formula presented.) admits a separating system consisting of (Formula presented.) paths, improving the previous almost linear bound of (Formula presented.), and settling conjectures posed by Balogh, Csaba, Martin, and Pluhár and by Falgas-Ravry, Kittipassorn, Korándi, Letzter, and Narayanan. We investigate a natural generalization of these results to subdivisions of cliques, showing that every graph admits both a separating system consisting of (Formula presented.) edges and cycles and a separating system consisting of (Formula presented.) edges and subdivisions of (Formula presented.).This study has been partially supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior ‐ Brasil ‐ CAPES ‐ Finance Code 001.Fábio Botler is supported by CNPq (304315/2022‐2) and CAPES (88881.973147/2024‐01). Tássio Naia was supported by the Grant PID2020‐113082GB‐I00funded by MICIU/AEI/10.13039/501100011033 and by the Spanish State Research Agency, through the Severo Ochoa and María de Maeztu Program forCenters and Units of Excellence in R&D (CEX2020‐001084‐M). CNPq is the National Council for Scientific and Technological Development of Brazil.info:eu-repo/semantics/publishedVersionJohn Wiley and Sons2025info:eu-repo/semantics/article7 p.application/pdfhttp://hdl.handle.net/2072/484458RECERCAT (Dipòsit de la Recerca de Catalunya)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésJournal of Graph TheoryAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2072/4844582026-05-29T05:05:01Z
dc.title.none.fl_str_mv Separating the Edges of a Graph by Cycles and by Subdivisions of K4
title Separating the Edges of a Graph by Cycles and by Subdivisions of K4
spellingShingle Separating the Edges of a Graph by Cycles and by Subdivisions of K4
Botler, F.
Graph
Separating system
Subdivision
51
title_short Separating the Edges of a Graph by Cycles and by Subdivisions of K4
title_full Separating the Edges of a Graph by Cycles and by Subdivisions of K4
title_fullStr Separating the Edges of a Graph by Cycles and by Subdivisions of K4
title_full_unstemmed Separating the Edges of a Graph by Cycles and by Subdivisions of K4
title_sort Separating the Edges of a Graph by Cycles and by Subdivisions of K4
dc.creator.none.fl_str_mv Botler, F.
Naia, Tássio
author Botler, F.
author_facet Botler, F.
Naia, Tássio
author_role author
author2 Naia, Tássio
author2_role author
dc.subject.none.fl_str_mv Graph
Separating system
Subdivision
51
topic Graph
Separating system
Subdivision
51
description A separating system of a graph (Formula presented.) is a family (Formula presented.) of subgraphs of (Formula presented.) for which the following holds: for all distinct edges (Formula presented.) and (Formula presented.) of (Formula presented.), there exists an element in (Formula presented.) that contains (Formula presented.) but not (Formula presented.). Recently, it has been shown that every graph of order (Formula presented.) admits a separating system consisting of (Formula presented.) paths, improving the previous almost linear bound of (Formula presented.), and settling conjectures posed by Balogh, Csaba, Martin, and Pluhár and by Falgas-Ravry, Kittipassorn, Korándi, Letzter, and Narayanan. We investigate a natural generalization of these results to subdivisions of cliques, showing that every graph admits both a separating system consisting of (Formula presented.) edges and cycles and a separating system consisting of (Formula presented.) edges and subdivisions of (Formula presented.).
publishDate 2025
dc.date.none.fl_str_mv 2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/2072/484458
url http://hdl.handle.net/2072/484458
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Graph Theory
dc.rights.none.fl_str_mv Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 7 p.
application/pdf
dc.publisher.none.fl_str_mv John Wiley and Sons
publisher.none.fl_str_mv John Wiley and Sons
dc.source.none.fl_str_mv RECERCAT (Dipòsit de la Recerca de Catalunya)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.811543

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