A recipe theorem for the topological Tutte polynomial of Bollobas and Riordan
| dc.creator | Ellis-Monaghan, Joanna A. | |
| dc.creator | Sarmiento, Irasema | |
| dc.date | 2009-03-15 | |
| dc.date.accessioned | 2026-07-07T12:52:46Z | |
| dc.date.available | 2026-07-07T12:52:46Z | |
| dc.description | In [A polynomial invariant of graphs on orientable surfaces, Proc. Lond. Math. Soc., III Ser. 83, No. 3, 513-531 (2001)] and [A polynomial of graphs on surfaces, Math. Ann. 323, 81-96 (2002)], Bollobas and Riordan generalized the classical Tutte polynomial to graphs cellularly embedded in surfaces, i.e. ribbon graphs, thus encoding topological information not captured by the classical Tutte polynomial. We provide a `recipe theorem' for their new topological Tutte polynomial, R(G). We then relate R(G) to the generalized transition polynomial Q(G) via a medial graph construction, thus extending the relation between the classical Tutte polynomial and the Martin, or circuit partition, polynomial to ribbon graphs. We use this relation to prove a duality property for R(G) that holds for both oriented and unoriented ribbon graphs. We conclude by placing the results of Chumutov and Pak [The Kauffman bracket and the Bollobas-Riordan polynomial of ribbon graphs, Moscow Mathematical Journal 7(3) (2007) 409-418] for virtual links in the context of the relation between R(G) and Q(R). | |
| dc.description | 23 pages, 10 figures, dedicated to Thomas Brylawski | |
| dc.identifier | https://arxiv.org/abs/0903.2643 | |
| dc.identifier | http://arxiv.org/abs/0903.2643 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223404 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C10; 07M15 | |
| dc.title | A recipe theorem for the topological Tutte polynomial of Bollobas and Riordan | |
| dc.type | text |