On the number of graphs not containing $K_{3,3}$ as a minor
| Autor: | Gerke, S., Gimenez, O., Noy, M., Weissl, A. |
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| Rok vydání: | 2008 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 17 pages |
| Databáze: | arXiv |
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