Colouring the Petals of a Graph

Colouring the Petals of a Graph

A petal graph is a connected graph G with maximum degree three, minimum degree two, and such that the set of vertices of degree three induces a 2–regular graph and the set of vertices of degree two induces an empty graph. We prove here that, with the single exception of the graph obtained from the Petersen graph by deleting one vertex, all petal graphs are Class 1. This settles a particular cas...

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...