The Bollobás–Riordan polynomial can mean a 3-variable invariant polynomial of graphs on orientable surfaces, or a more general 4-variable invariant of ribbon graphs, generalizing the Tutte polynomial.
These polynomials were discovered by Béla Bollobás and Oliver Riordan (2001, 2002).
The 3-variable Bollobás–Riordan polynomial of a graph
{\displaystyle G}
is given by where the sum runs over all the spanning subgraphs