Random cubic planar graphs revisited

The goal of our work is to analyze random cubic planar graphs according to the uniform distribution. More precisely, let G be the class of labelled cubic planar graphs and let gn be the number of graphs with n vertices. Then each graph in G with n vertices has the same probability 1/gn. This model was analyzed first by Bodirsky et al. [1], and here we revisit and extend their work. The motivation for this revision is twofold. First, some proofs in [1] where incomplete with respect to the singularity analysis and we aim at providing full proofs. Secondly, we obtain new results that considerably strengthen those in [1] and shed more light on the structure of random cubic planar graphs. We present a selection of our results on asymptotic enumeration and on limit laws for parameters of random graphs.