Defective and Clustered Graph Colouring

Clustered Colouring in Minor-Closed Classes

The clustered chromatic number of a class of graphs is the minimum integer k such that for some integer c every graph in the class is k-colourable with monochromatic components of size at most c. We prove that for every graph H , the clustered chromatic number of the class of H-minor-free graphs is tied to the tree-depth of H . In particular, if H has tree-depth t then every H-minor-free graph ...

Colouring a Graph Frugally

Evolutionary Graph Colouring

The problem we are addressing in this paper was proposed at SIROCCO’98 by Kranakis [1], with possible applications to finding a consensus in distributive networks. The problem can be viewed as a simple game on graphs, in a way similar to the game of life. The aim is to colour all vertices of a graph, which are initially coloured with three colours 0,1, and 2, with a single colour. The only rule...

Graph colouring algorithms

This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available techniques and is organized by algorithmic paradigm.

Online Graph Colouring

This paper considers the problem of online graph colouring. An algorithm for vertex-colouring graphs is said to be online if each vertex is irrevocably assigned a colour before later vertices are considered. We first introduce the problem formally and define a perfomance metric to evaluate the success of an online colouring algorithm. Then, several upper and lower bounds are presented on the pe...