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dc.contributor.authorNoy Serrano, Marcos
dc.contributor.authorRequile, Clement
dc.contributor.authorRué Perna, Juan José
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2023-10-24T15:43:24Z
dc.date.available2023-10-24T15:43:24Z
dc.date.issued2023-05
dc.identifier.citationNoy, M.; Requilé, C.; Rue, J. Enumeration of labelled 4-regular planar graphs II: asymptotics. "European journal of combinatorics", Maig 2023, vol. 110, núm. article 103661.
dc.identifier.issn0195-6698
dc.identifier.otherhttps://arxiv.org/abs/2001.05943
dc.identifier.urihttp://hdl.handle.net/2117/395317
dc.description.abstractThis 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.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
dc.subject.lcshCombinatorial analysis
dc.titleEnumeration of labelled 4-regular planar graphs II: asymptotics
dc.typeArticle
dc.subject.lemacCombinacions (Matemàtica)
dc.contributor.groupUniversitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics
dc.identifier.doi10.1016/j.ejc.2022.103661
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::05 Combinatorics
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/abs/pii/S0195669822001573
dc.rights.accessOpen Access
local.identifier.drac35139543
dc.description.versionPostprint (author's final draft)
dc.relation.projectidinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-82166-P/ES/COMBINATORIA GEOMETRICA, ALGEBRAICA Y PROBABILISTICA/
dc.relation.projectidinfo:eu-repo/grantAgreement/MINECO//MDM-2014-0445/ES/Barcelona Graduate School of Mathematics (BGSMath)/
dc.relation.projectidinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113082GB-I00/ES/COMBINATORIA: NUEVAS TENDENCIAS Y APLICACIONES/
local.citation.authorNoy, M.; Requilé, Clément; Rue, J.
local.citation.publicationNameEuropean journal of combinatorics
local.citation.volume110
local.citation.numberarticle 103661


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