{"document_url": "https://en.wikipedia.org/wiki/Bollob%C3%A1s%E2%80%93Riordan_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.

History

These polynomials were discovered by Béla Bollobás and Oliver Riordan (2001, 2002).

Formal definition

The 3-variable Bollobás–Riordan polynomial of a graph
is given by
,

where the sum runs over all the spanning subgraphs
and