The study and recognition of graph families (or graph properties) is an essential part of combinatorics. Graph colouring is another fundamental concept of graph theory that can be looked at, in large part, as the recognition of a family of graphs that are colourable according to certain rules. In this thesis, we study additive induced-hereditary families, and some generalisations, from a colour...

This paper presents a hybrid evolutionary algorithm to tackle university course timetabling problems. The proposed approach is an extension of a non-linear great deluge algorithm in which evolutionary operators are incorporated. First, we generate a population of feasible solutions using a tailored process that incorporates heuristics for graph colouring and assignment problems. That initialisa...

A major problem related to combinatorial optimization and population-based algorithms is the functional degeneracy of the search for problems with a high degree of symmetry. The population may in fact present multiple permutations of the same solutions which bound the exploration of the solution space. A genetic algorithm (GA) cannot generally cope with this problem unless additional mechanisms...

In this paper, we study a colouring problem motivated by a practical frequency assignment problem and up to our best knowledge new. In wireless networks, a node interferes with the other nodes the level of interference depending on numerous parameters: distance between the nodes, geographical topography, obstacles, etc. We model this with a weighted graph G where the weights on the edges repres...

Research was conducted in a certified organic apple (Malus x domestica Borkh.) orchard in 2000 to determine the effect of organic pest management techniques on pest control, apple yields and microbial populations on harvested apples. In Experiment I, apple colouring bags, sticky red spheres, kaolin particle film, kaolin particle film plus sticky red spheres, or colouring bags plus sticky red sp...

A colouring of a 4-cycle system (V,B) is a surjective mapping φ : V → Γ. The elements of Γ are colours. If |Γ| = m, we have an m-colouring of (V,B). For every B ∈ B, let φ(B) = {φ(x)|x ∈ B}. There are seven distinct colouring patterns in which a 4-cycle can be coloured: type a (××××, monochromatic), type b (×××2, two-coloured of pattern 3 + 1), type c (× × 22, two-coloured of pattern 2 + 2), ty...

For a fixed graph $H$, the reconfiguration problem for $H$-colourings (i.e. homomorphisms to $H$) asks: given a graph $G$ and two $H$-colourings $\varphi$ and $\psi$ of $G$, does there exist a sequence $f_0,\dots,f_m$ of $H$-colourings such that $f_0=\varphi$, $f_m=\psi$ and $f_i(u)f_{i+1}(v)\in E(H)$ for every $0\leq i<m$ and $uv\in E(G)$? If the graph $G$ is loop-free, then this is the equiva...

The Channel Assignment Problem is an NP-complete problem to assign a minimum number of channels under certain constraints to requested calls in a cellular radio system. Examples of the many approaches to solve this problem include using neural-networks, simulated annealing, graph colouring, genetic algorithms, and heuristic searches. We present a new heuristic algorithm that consists of three s...

This article introduces a natural extension of colouring numbers of knots, called colouring polynomials, and studies their relationship to Yang-Baxter invariants and quandle 2-cocycle invariants. For a knot K in the 3-sphere let πK be the fundamental group of the knot complement S 3 rK, and let mK , lK ∈ πK be a meridian-longitude pair. Given a finite group G and an element x ∈ G we consider th...

The author explores the application of graph colouring to biological networks, specifically protein-protein interaction (PPI) networks. First, the author finds that given similar conditions (i.e. graph size, degree distribution and clustering), fewer colours are needed to colour disassortative than assortative networks. Fewer colours create fewer independent sets which in turn imply higher conc...