The Kauffman bracket of virtual links and the Bollobás–Riordan polynomial

We show that the Kauffman bracket $[L]$ of a checkerboard colorable virtual link $L$ is an evaluation of the Bollobás–Riordan polynomial $R_{G_L}$ of a ribbon graph associated with $L$. This result generalizes the celebrated relation between the classical Kauffman bracket and the Tutte polynomial of planar graphs.