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{\bf Stefanie Gerke, Omer Gim\'enez, Marc Noy and Andreas Wei{\ss}l}
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{\bf The Number of Graphs Not Containing $K_{3,3}$ as a Minor}
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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 number of
edges. To establish these results, we translate a decomposition for
the corresponding graphs 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.
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