skip to content

The topological Tutte polynomials of Bollobas and Riordan: properties and relations to other graph polynomials

Presented by: 
I Sarmiento [Roma Tor Vergata]
Wednesday 23rd January 2008 - 16:00 to 16:30
INI Seminar Room 1

In [BR01], [BR02], Bollob´as and Riordan defined analogs of the Tutte polynomial for graphs embedded in surfaces, thus encoding topological information lost in the classical Tutte polynomial. We pro- vide a ‘recipe theorem’ for these polynomials and use it to relate them to the generalized transition polynomial, the topological Tutte poly- nomials defined in [Las75], [Las78], [Las79], the parametrized Tutte polynomial of [Zas92] and [BR99], and Bouchet’s Tutte-Martin poly- nomial of isotropic systems. Various evaluations of these polynomi- als of Bollob´as and Riordan, as well as insight into the topological information they encode. The relationship between the generalized transition polynomial and the topological Tutte polynomial extends a result of [Jae90] from planar graphs to arbitrary graphs by giving a relationship between the transition and the R polynomials. We also visit the Kauffman bracket in light of these relationships and that es- tablished between it and the topolofical Tutte polynomial in [CP].

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons