turkmath.org

The chromatic polynomial of a graph $G$, denoted by $\pi(G,x)$, is the polynomial whose evaluations at positive integers $x$ count the number of proper $x$-colourings of $G$. This polynomial was introduced by Birkhoff in 1912 in an attempt to prove the famous Four Colour Theorem which stood as an unsolved problem for over a century. Since then, the chromatic polynomial has been extensively studied and it has become an important object in the study of combinatorics. In this talk, I will discuss several problems on the chromatic polynomial and other related graph polynomials, and give an overview of some recent results.