Algebraic Graph Theory Seminar - Logan Crew

Title: A New Graph Polynomial from the Chromatic Symmetric Function

Abstract:

The chromatic symmetric function X_G of a graph generalizes the chromatic polynomial by distinguishing proper n-colourings by how many times each colour is used. Furthermore, many other natural graph polynomials also arise from specializations of X_G; we will focus on a new one called the tree polynomial, which we show has reciprocity and duality-like relations with the chromatic polynomial, and counts certain proper colourings of spanning subgraphs of G.

This is joint work with William Chan.