Enumeration of chordal planar graphs and maps

We determine the number of labelled chordal planar graphs with n vertices, which is asymptotically g⋅n−5/2γnn! for a constant g>0 and γ≈11.89235. We also determine the number of rooted simple chordal planar maps with n edges, which is asymptotically s⋅n−3/2δn, where s>0, δ=1/σ≈6.40375,...

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Detalles Bibliográficos
Autores: Castellví, J., Noy, M., Requilé, C.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/534626
Acceso en línea:http://hdl.handle.net/2072/534626
Access Level:acceso abierto
Palabra clave:Asymptotic enumeration, Chordal planar graphs, Subcritical graph class
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spelling Enumeration of chordal planar graphs and mapsCastellví, J.Noy, M.Requilé, C.Asymptotic enumeration, Chordal planar graphs, Subcritical graph classWe determine the number of labelled chordal planar graphs with n vertices, which is asymptotically g⋅n−5/2γnn! for a constant g>0 and γ≈11.89235. We also determine the number of rooted simple chordal planar maps with n edges, which is asymptotically s⋅n−3/2δn, where s>0, δ=1/σ≈6.40375, and σ is an algebraic number of degree 12. The proofs are based on combinatorial decompositions and singularity analysis. Chordal planar graphs (or maps) are a natural example of a subcritical class of graphs in which the class of 3-connected graphs is relatively rich. The 3-connected members are precisely chordal triangulations, those obtained starting from K4 by repeatedly adding vertices adjacent to an existing triangular face. © 2022 The Author(s)We gratefully acknowledge earlier discussions on this project with Erkan Narmanli. M.N. was supported by grants MTM2017-82166-P and PID2020-113082GB-I00, the Severo Ochoa and Mar´ıa de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M). C.R. was supported by the grant Beatriu de Pin´os BP2019, funded by the H2020 COFUND project No 801370 and AGAUR (the Catalan agency for management of university and research grants), and the grant PID2020-113082GB-I00 of the Spanish ministry of Science and Innovation.Elsevier B.V.2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion10 p.application/pdfhttp://hdl.handle.net/2072/534626RECERCAT (Dipòsit de la Recerca de Catalunya)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésDiscrete MathematicsL'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2072/5346262026-05-29T05:05:01Z
dc.title.none.fl_str_mv Enumeration of chordal planar graphs and maps
title Enumeration of chordal planar graphs and maps
spellingShingle Enumeration of chordal planar graphs and maps
Castellví, J.
Asymptotic enumeration, Chordal planar graphs, Subcritical graph class
title_short Enumeration of chordal planar graphs and maps
title_full Enumeration of chordal planar graphs and maps
title_fullStr Enumeration of chordal planar graphs and maps
title_full_unstemmed Enumeration of chordal planar graphs and maps
title_sort Enumeration of chordal planar graphs and maps
dc.creator.none.fl_str_mv Castellví, J.
Noy, M.
Requilé, C.
author Castellví, J.
author_facet Castellví, J.
Noy, M.
Requilé, C.
author_role author
author2 Noy, M.
Requilé, C.
author2_role author
author
dc.subject.none.fl_str_mv Asymptotic enumeration, Chordal planar graphs, Subcritical graph class
topic Asymptotic enumeration, Chordal planar graphs, Subcritical graph class
description We determine the number of labelled chordal planar graphs with n vertices, which is asymptotically g⋅n−5/2γnn! for a constant g>0 and γ≈11.89235. We also determine the number of rooted simple chordal planar maps with n edges, which is asymptotically s⋅n−3/2δn, where s>0, δ=1/σ≈6.40375, and σ is an algebraic number of degree 12. The proofs are based on combinatorial decompositions and singularity analysis. Chordal planar graphs (or maps) are a natural example of a subcritical class of graphs in which the class of 3-connected graphs is relatively rich. The 3-connected members are precisely chordal triangulations, those obtained starting from K4 by repeatedly adding vertices adjacent to an existing triangular face. © 2022 The Author(s)
publishDate 2022
dc.date.none.fl_str_mv 2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/2072/534626
url http://hdl.handle.net/2072/534626
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Discrete Mathematics
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 10 p.
application/pdf
dc.publisher.none.fl_str_mv Elsevier B.V.
publisher.none.fl_str_mv Elsevier B.V.
dc.source.none.fl_str_mv RECERCAT (Dipòsit de la Recerca de Catalunya)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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