  We establish a relation between the Bollobas-Riordan polynomial of a ribbon
graph with the relative Tutte polynomial of a plane graph obtained from the
ribbon graph using its projection to the plane in a nontrivial way. Also we
give a duality formula for the relative Tutte polynomial of dual plane graphs
and an expression of the Kauffman bracket of a virtual link as a specialization
of the relative Tutte polynomial.
