On the number of genus one labeled circle trees
| dc.creator | Meszaros, Karola | |
| dc.date | 2005-09-18 | |
| dc.date.accessioned | 2026-07-07T06:18:10Z | |
| dc.date.available | 2026-07-07T06:18:10Z | |
| dc.description | A genus one labeled circle tree is a tree with its vertices on a circle, such that together they can be embedded in a surface of genus one, but not of genus zero. We define an e-reduction process whereby a special type of subtree, called an e-graph, is collapsed to an edge. We show that genus is invariant under e-reduction. Our main result is a classification of genus one labeled circle trees through e-reduction. Using this we prove a modified version of a conjecture of David Hough, namely, that the number of genus one labeled circle trees on $n$ vertices is divisible by $n$ or if it is not divisible by $n$ then it is divisible by $n/2$. Moreover, we explicitly characterize when each of these possibilities occur. | |
| dc.description | 32 pages, 30 figures | |
| dc.identifier | https://arxiv.org/abs/math/0509407 | |
| dc.identifier | http://arxiv.org/abs/math/0509407 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94644 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A99 | |
| dc.title | On the number of genus one labeled circle trees | |
| dc.type | text |