Estimating the Growth Constant of Labelled Planar Graphs
Omer Giménez, Marc Noy · Birkhäuser Basel eBooks · 2004
Let Gn be the number of labelled planar graphs on n vertices and $$ \gamma = \lim _{n \to \infty } \left( {G_n /n!} \right)^{1/n} $$ .It is known that 26.1848<<30.0606. In this paper we sharpen these bounds to 27.22685<<27.22688. The proof is based on recent results of Bender, Gao and Wormald [Elec. J. Combinatorics 9 (2002) R43], and on singularity analysis of generating functions