We study various properties of the random planar graph Rn, drawn uniformly at random from
the class Pn of all simple planar graphs on n labelled vertices. In particular, we show that the …

Generating random networks efficiently and accurately is an important challenge for
practical applications, and an interesting question for theoretical study. This book presents …

We prove a generalization of Kirchhoff's matrix-tree theorem in which a large class of
combinatorial objects are represented by non-Gaussian Grassmann integrals. As a special …

The family of well-orderly maps is a family of planar maps with the property that every
connected planar graph has at least one plane embedding which is a well-orderly map. We …

This article introduces new algorithms for the uniform random generation of labelled planar
graphs. Its principles rely on Boltzmann samplers, as recently developed by Duchon …

We show that the number of labeled cubic planar graphs on n vertices with n even is
asymptotically αn− 7/2ρ− nn!, where ρ− 1≐ 3.13259 and α are analytic constants. We show …

Tutte has described in the book" Connectivity in graphs" a canonical decomposition of any
graph into 3-connected components. In this article we translate (using the language of …

Counting labelled planar graphs, and typical properties of random labelled planar graphs,
have received much attention recently. We start the process here of extending these …

We study various properties of a random graph R n, drawn uniformly at random from the
class A _n of all simple graphs on n labelled vertices that satisfy some given property, such …

Cette these traite de l'algorithmique des cartes planaires (graphes dessinés dans le plan
sans intersection d'arêtes) et propose des procédures efficaces pour le codage, la …