The Universal Form of the Tutte Polynomial

The Tutte polynomial is a powerful tool from matroid theory. It can be specialized to obtain matroid invariants including the cardinality of ground set, the number of spanning sets, and the the number of bases. In this talk, we focus on graphic matroids and present Bollobás' result characterization of the ''universal form of the Tutte polynomial.'' Bollobás' theorem gives a way to describe certain isomorphism invariants as specializations of the Tutte polynomial of the graphic matroid. No prior knowledge about matroids will be assumed, although some knowledge of graph theory will be assumed. This is a pre-talk for the combinatorics seminar on Friday.