Geodesic
The number of graphs not containing \(K_{3,3}\) as a minor
The electronic journal of combinatorics, Tome 15 (2008)

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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.
DOI : 10.37236/838
Classification : 05C30, 05C35, 05A16
Mots-clés : symptotic estimates, number of labelled graphs, generating functions 
Stefanie Gerke; Omer Giménez; Marc Noy; Andreas Weißl. The number of graphs not containing \(K_{3,3}\) as a minor. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/838
@article{10_37236_838,
     author = {Stefanie Gerke and Omer Gim\'enez and Marc Noy and Andreas Wei{\ss}l},
     title = {The number of graphs not containing {\(K_{3,3}\)} as a minor},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/838},
     zbl = {1163.05319},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/838/}
}
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