
Nicolas Pouyanne,
University of Versailles

"Enumeration of planar graphs"
A graph is called planar when it can be embedded into the plane so that no two edges cross at an interior point.
How does a planar graph with n vertices look like when n grows to infinity?
Using generating functions and analytic combinatorics, it will be
shown how can one reach results such as:
 give an asymptotic equivalent of the number of planar graphs;
 the number of edges of a planar graph satisfies a central limit
theorem with linear mean and variance;
 the number of connected components of an planar graph is
asymptotically Poisson distributed.
Bibliography :
 O. Gimenez and M. Noy, Asymptotic enumeration and limit laws of planar graphs, Journal AMS, vol.22, n.2, 309329 (2009).
 E.A. Bender, Z. Gao, N.C. Wormald, The number of 2connected labeled planar graphs, Elec. J. Combin. 9, R43, (2002).
 P. Flajolet and R. Sedgewick, Analytic Combinatorics, Cambridge
Univ. Press (2008).