Enumeration of chordal planar graphs and maps

• Jordi Castellví ^[1] ; Marc Noy ^[1] ; Clément Requilé ^[2]
  1. [1] Universitat Politècnica de Catalunya

     Universitat Politècnica de Catalunya

     Barcelona, España

     
  2. [2] Center for Mathematical Research (CRM), Barcelona, Spain
• Localización: Discrete Mathematics Days 2022 / Luis Felipe Tabera Alonso (ed. lit.), 2022, ISBN 978-84-19024-02-2, págs. 77-83
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We determine the number of labelled chordal planar graphs with n vertices, which isasymptotically c1 · n−5/2γnn! for a constant c1 > 0 and γ ≈ 11.89235. We also determinethe number of rooted simple chordal planar maps with n edges, which is asymptoticallyc2n−3/2δn, where δ = 1/σ ≈ 6.40375, and σ is an algebraic number of degree 12. Theproofs are based on combinatorial decompositions and singularity analysis. Chordal planargraphs (or maps) are a natural example of a subcritical class of graphs in which the classof 3-connected graphs is relatively rich. The 3-connected members are precisely chordaltriangulations, those obtained starting from K4 by repeatedly adding vertices adjacent toan existing triangle.