On the number of K3,3-minor-free and maximal K3,3-minor-free graphs

In this paper we derive precise asymptotic estimates for the number of simple labeled K3,3-minor-free and maximal K3,3minor-free graphs on n vertices. Additionally, we establish limit laws for parameters in random K3,3-minor-free graphs, as for instance the expected number of edges. To establish these results, we translate a decomposition for the corresponding graph class into equations for generating functions and use singularity analysis.