On the number of graphs not containing $K_{3,3}$ as a minor
| dc.creator | Gerke, S. | |
| dc.creator | Gimenez, O. | |
| dc.creator | Noy, M. | |
| dc.creator | Weissl, A. | |
| dc.date | 2008-03-31 | |
| dc.date | 2008-04-01 | |
| dc.date.accessioned | 2026-07-07T09:29:25Z | |
| dc.date.available | 2026-07-07T09:29:25Z | |
| dc.description | 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. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/0803.4418 | |
| dc.identifier | http://arxiv.org/abs/0803.4418 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157778 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C30 | |
| dc.title | On the number of graphs not containing $K_{3,3}$ as a minor | |
| dc.type | text |