论文信息 - Estimating the Growth Constant of Labelled Planar Graphs

Estimating the Growth Constant of Labelled Planar Graphs

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

Marc Noy | Omer Giménez | Omer Giménez | M. Noy

[1] F. B. Hildebrand,et al. Introduction To Numerical Analysis , 1957 .

[2] R. Mullin,et al. The enumeration of c-nets via quadrangulations , 1968 .

[3] Timothy R. S. Walsh,et al. Counting labelled three-connected and homeomorphically irreducible two-connected graphs , 1982, J. Comb. Theory, Ser. B.

[4] Edward A. Bender,et al. The Number of Labeled 2-Connected Planar Graphs , 2002, Electron. J. Comb..

[5] Deryk Osthus,et al. On random planar graphs, the number of planar graphs and their triangulations , 2003, J. Comb. Theory, Ser. B.

[6] Nicolas Bonichon,et al. An Information-Theoretic Upper Bound of Planar Graphs Using Triangulation , 2003, STACS.

[7] I. Goulden,et al. Combinatorial Enumeration , 2004 .

[8] Colin McDiarmid,et al. On the Number of Edges in Random Planar Graphs , 2004, Combinatorics, Probability and Computing.

[9] Colin McDiarmid,et al. Random planar graphs , 2005, J. Comb. Theory B.