Enumeration of labelled 4-regular planar graphs
We present the first combinatorial scheme for counting labelled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function of labelled 4-regular planar graphs can be computed effectively as the solution of a system of equation...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2019 |
| 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:2117/191331 |
| Acesso em linha: | https://hdl.handle.net/2117/191331 https://dx.doi.org/10.1112/plms.12234 |
| Access Level: | acceso abierto |
| Palavra-chave: | Planar graphs Classificació AMS::05 Combinatorics::05C Graph theory Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Resumo: | We present the first combinatorial scheme for counting labelled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function of labelled 4-regular planar graphs can be computed effectively as the solution of a system of equations, from which the coefficients can be extracted. As a byproduct, we also enumerate labelled 3-connected 4-regular planar graphs, and simple 4-regular rooted maps. |
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