Title: Two approaches to virtual Thistlethwaite's theorem

Abstract.
There are two different generalizations of Thistlethwaite's theorem to 
virtual links. One is based on ribbon graphs and a topological version 
of the Tutte polynomial due  to B.Bollobas and O.Riordan. Another involves 
a relative version of the Tutte polynomial of plane graphs found by Y.Diao 
and G.Hetyei. I explain a direct relation between the Bollobas--Riordan 
of ribbon graphs and relative Tutte polynomials plane graphs. This is a 
joint work with Clark Butler.