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...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/395317 |
| Acesso em linha: | https://hdl.handle.net/2117/395317 https://dx.doi.org/10.1016/j.ejc.2022.103661 |
| Access Level: | acceso abierto |
| Palavra-chave: | Combinatorial analysis Combinacions (Matemàtica) Classificació AMS::05 Combinatorics Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria |
| Resumo: | 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. |
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