Bollobás–Riordan polynomial

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