Thomas Perrett: Graph colouring is a central topic in graph theory which has numerous real world applications. Quantitative information about the colourings of graphs is contained in an algebraic object called the chromatic polynomial, which was introduced by Birkhoff in 1917.
It was hoped that studying the roots of the chromatic polynomial could lead to an algebraic proof of the famous Four Colour Theorem, however this hope has not yet been realised. Nevertheless several interesting results have been obtained regarding the distribution of these roots, and new connections to statistical physics have arisen as a result. One of the main aims of this project is to obtain further results on these polynomials and their roots when the graph in question has certain structural properties.
Effective start/end date 01/10/2013 → 16/08/2017
Publised as PhD report: Roots of the Chromatic Polynomial
Supervisor: Carsten Thomassen
Algolog section