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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Bibliographic Details
Authors: Castellví, J., Noy, M., Requilé, C.
Format: article
Status:Published version
Publication Date:2022
Country:España
Institution:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repository:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/534626
Online Access:http://hdl.handle.net/2072/534626
Access Level:Open access
Keyword:Asymptotic enumeration, Chordal planar graphs, Subcritical graph class
Description
Summary: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)

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