## Anagram-free Graph Colouring and Colour Schemes

thesis

posted on 26.02.2019 by TIMOTHY EDWARD WILSON#### thesis

In order to distinguish essays and pre-prints from academic theses, we have a separate category. These are often much longer text based documents than a paper.

Graphs model the connectivity of networks, and many researchers study how to colour the nodes of a graph under various restrictions. Anagram-free colouring is a type of graph colouring which requires the first half of every path through a graph to not be a permutation of the second half. This thesis answers questions about the number of colours required to anagram-free colour many types of graphs. It also studies anagram-free colouring in a wider context by introducing colour schemes, an axiomatic approach that unifies known types of graph colouring.