Mathematical Sciences - Colloquium - Bruce Sagan, (Michigan State University) "The protean chromatic polynomial"

Friday, April 05, 2019
11:00 am to 11:50 am


Floor/Room #: 

Title: The protean chromatic polynomial

Speaker: Bruce E. Sagan (Michigan State University)

ABSTRACT: Let t be a positive integer and let G be a combinatorial graph with vertices V and edges E. A proper coloring of G from a set with t colors is a function c : V → {1, 2, …, t} such that if uv ϵ E then c(u)c(v), that is, the endpoints of an edge must be colored differently. These are the colorings considered in the famous Four Color Theorem. The chromatic polynomial of G, P(G; t), is the number of proper colorings of G from a set with t colors. It turns out that this is a polynomial in t with many amazing properties. One can characterize the degree and coefficients of P(G; t). There are also connections with acyclic orientations, increasing spanning forests, hyperplane arrangements, symmetric functions, and Chern classes in algebraic geometry. This talk will survey some of these results.