Matroid Theory Seminar - Iian Moffatt

Title: Matroid perspectives and graph polynomials

Abstract: Many graph polynomials can be extended to matroid polynomials. The more general setting of matroids allows us to access and understand properties of the graph version of the polynomial that may have otherwise been obscured. It is well-known that the Tutte polynomial can be understood as a matroid polynomial. In this talk I will describe how Las Vergnas' matroid perspectives can be used to obtain a matroidal framework for B.~Bollob\'as and O.~Riordan's, and for Krushkal's extensions of the Tutte polynomial to embedded graphs. I will also describe some of the advantages of this more general framework.