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...

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Detalles Bibliográficos
Autores: Noy Serrano, Marcos|||0000-0002-2399-1359, Requilé, Clément, Rué Perna, Juan José|||0000-0002-6420-3179
Tipo de recurso: artículo
Fecha de publicación:2019
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:2117/191331
Acceso en línea:https://hdl.handle.net/2117/191331
https://dx.doi.org/10.1112/plms.12234
Access Level:acceso abierto
Palabra clave:Planar graphs
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística
Descripción
Sumario: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.