  For a graph G embedded in an orientable surface \Sigma, we consider
associated links L(G) in the thickened surface \Sigma \times I. We relate the
HOMFLY polynomial of L(G) to the recently defined Bollobas-Riordan polynomial
of a ribbon graph. This generalizes celebrated results of Jaeger and Traldi. We
use knot theory to prove results about graph polynomials and, after discussing
questions of equivalence of the polynomials, we go on to use our formulae to
prove a duality relation for the Bollobas-Riordan polynomial. We then consider
the specialization to the Jones polynomial and recent results of Chmutov and
Pak to relate the Bollobas-Riordan polynomials of an embedded graph and its
tensor product with a cycle.
