Enumeration of labelled 4-regular planar graphs II: asymptotics

This work is a follow-up of the article (Noy et al., 2019), where the authors solved the problem of counting labelled 4-regular planar graphs. In this paper, we obtain a precise asymptotic estimate for the number of labelled 4-regular planar graphs on vertices. Our estimate is of the form , where is...

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Detalles Bibliográficos
Autores: Noy Serrano, Marcos|||0000-0002-2399-1359, Requile, Clement|||0000-0002-7689-7972, Rué Perna, Juan José|||0000-0002-6420-3179
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/395317
Acceso en línea:https://hdl.handle.net/2117/395317
https://dx.doi.org/10.1016/j.ejc.2022.103661
Access Level:acceso abierto
Palabra clave:Combinatorial analysis
Combinacions (Matemàtica)
Classificació AMS::05 Combinatorics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
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spelling Enumeration of labelled 4-regular planar graphs II: asymptoticsNoy Serrano, Marcos|||0000-0002-2399-1359Requile, Clement|||0000-0002-7689-7972Rué Perna, Juan José|||0000-0002-6420-3179Combinatorial analysisCombinacions (Matemàtica)Classificació AMS::05 CombinatoricsÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::CombinatòriaThis work is a follow-up of the article (Noy et al., 2019), where the authors solved the problem of counting labelled 4-regular planar graphs. In this paper, we obtain a precise asymptotic estimate for the number of labelled 4-regular planar graphs on vertices. Our estimate is of the form , where is a constant and is the radius of convergence of the generating function , and conforms to the universal pattern obtained previously in the enumeration of several classes of planar graphs. In addition to analytic methods, our solution needs intensive use of computer algebra in order to deal with large systems of multivariate polynomial equations. We also obtain asymptotic estimates for the number of 2- and 3-connected 4-regular planar graphs, and for the number of 4-regular simple maps, both connected and 2-connected.Peer Reviewed20232023-05-0120232023-10-24journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/395317https://dx.doi.org/10.1016/j.ejc.2022.103661reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-82166-P COMBINATORIA GEOMETRICA, ALGEBRAICA Y PROBABILISTICAMinisterio de Economía y Competitividad http://doi.org/10.13039/501100003329 MDM-2014-0445 Barcelona Graduate School of Mathematics (BGSMath)Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113082GB-I00 COMBINATORIA: NUEVAS TENDENCIAS Y APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3953172026-05-27T15:37:01Z
dc.title.none.fl_str_mv Enumeration of labelled 4-regular planar graphs II: asymptotics
title Enumeration of labelled 4-regular planar graphs II: asymptotics
spellingShingle Enumeration of labelled 4-regular planar graphs II: asymptotics
Noy Serrano, Marcos|||0000-0002-2399-1359
Combinatorial analysis
Combinacions (Matemàtica)
Classificació AMS::05 Combinatorics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
title_short Enumeration of labelled 4-regular planar graphs II: asymptotics
title_full Enumeration of labelled 4-regular planar graphs II: asymptotics
title_fullStr Enumeration of labelled 4-regular planar graphs II: asymptotics
title_full_unstemmed Enumeration of labelled 4-regular planar graphs II: asymptotics
title_sort Enumeration of labelled 4-regular planar graphs II: asymptotics
dc.creator.none.fl_str_mv Noy Serrano, Marcos|||0000-0002-2399-1359
Requile, Clement|||0000-0002-7689-7972
Rué Perna, Juan José|||0000-0002-6420-3179
author Noy Serrano, Marcos|||0000-0002-2399-1359
author_facet Noy Serrano, Marcos|||0000-0002-2399-1359
Requile, Clement|||0000-0002-7689-7972
Rué Perna, Juan José|||0000-0002-6420-3179
author_role author
author2 Requile, Clement|||0000-0002-7689-7972
Rué Perna, Juan José|||0000-0002-6420-3179
author2_role author
author
dc.subject.none.fl_str_mv Combinatorial analysis
Combinacions (Matemàtica)
Classificació AMS::05 Combinatorics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
topic Combinatorial analysis
Combinacions (Matemàtica)
Classificació AMS::05 Combinatorics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
description This work is a follow-up of the article (Noy et al., 2019), where the authors solved the problem of counting labelled 4-regular planar graphs. In this paper, we obtain a precise asymptotic estimate for the number of labelled 4-regular planar graphs on vertices. Our estimate is of the form , where is a constant and is the radius of convergence of the generating function , and conforms to the universal pattern obtained previously in the enumeration of several classes of planar graphs. In addition to analytic methods, our solution needs intensive use of computer algebra in order to deal with large systems of multivariate polynomial equations. We also obtain asymptotic estimates for the number of 2- and 3-connected 4-regular planar graphs, and for the number of 4-regular simple maps, both connected and 2-connected.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-05-01
2023
2023-10-24
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/395317
https://dx.doi.org/10.1016/j.ejc.2022.103661
url https://hdl.handle.net/2117/395317
https://dx.doi.org/10.1016/j.ejc.2022.103661
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-82166-P COMBINATORIA GEOMETRICA, ALGEBRAICA Y PROBABILISTICA
Ministerio de Economía y Competitividad http://doi.org/10.13039/501100003329 MDM-2014-0445 Barcelona Graduate School of Mathematics (BGSMath)
Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113082GB-I00 COMBINATORIA: NUEVAS TENDENCIAS Y APLICACIONES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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