%0 Journal Article
%T On the number of graphs not containing $K_{3,3}$ as a minor
%A S. Gerke
%A O. Gimenez
%A M. Noy
%A A. Weissl
%J Mathematics
%D 2008
%I arXiv
%X We derive precise asymptotic estimates for the number of labelled graphs not containing $K_{3,3}$ as a minor, and also for those which are edge maximal. Additionally, we establish limit laws for parameters in random $K_{3,3}$-minor-free graphs, like 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. We also find a precise estimate for the number of graphs not containing the graph $K_{3,3}$ plus an edge as a minor.
%U http://arxiv.org/abs/0803.4418v2