Resumen de Enumeration of chordal planar graphs and maps

Jordi Castellví, Marc Noy Serrano, Clément Requilé

• 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.