Marc Noy1
Let be a graph chosen uniformly at random among all labelled planar graphs
with
vertices. Which are the typical properties of such a random planar
graph?
We show that has about
edges, where
is a constant
completely determined, and that deviations from
are with high
probability of small order. Among other properties, we also show that
is
connected with probability tending to a constant
The basic technique we use in the proofs is singularity analysis of counting generating functions, considered as complex valued functions.