Perfect 1-Factorisations A matching in a graph $G$ is a subset $M \subseteq E(G)$ of the edge set of $G$ such that no two edges of $M$ share a vertex. A 1-factor of a graph $G$ is a matching $F$

Title: Families of graphs containing only finitely many vertex-critical graphs. In this talk, motivated by algorithmic aspects of graph colouring, we will consider the problem of classifying vertex-critical graphs in families of graphs. We will complete a dichotomy theorem for

The Average Order of Dominating Sets of a Graph This talk focuses on the average order of dominating sets of a graph. We find the extremal graphs for the maximum and minimum value over all graphs on n vertices, while

Equitably colourable cycle decompositions A $c$-colouring of a decomposition of a graph $G$ is an assignment of $c$ colours to the vertices of $G$. A colouring is equitable if each colour is represented (as closely as possible) an equal number

Orthogonal Colourings of Graphs Two colourings of a graph are orthogonal if they have the property that when two vertices receive the same colour in one colouring, then those vertices receive distinct colours in the other colouring. In this talk,

Gracefully labelling windmills using Skolem-like sequences To gracefully label a graph G, assign each vertex v ∊ V(G) a distinct label l(v) from {0,1,2,...,|E(G)|}, such that {|l(u)-l(v)| : uv ∊ E(G)}={1,2,3,...,|E(G)|}. In this talk we will examine constructive techniques using

The Cheating Robot and Insider Information Throughout this talk, we explore a deterministic model as an alternative approach to studying simultaneous play combinatorial games. We call this the Cheating Robot model. This model forces both players to move at the

The Iterated Local Model for Social Networks Complex networks are said to exhibit four key properties: large scale, evolving over time, small world properties, and power law degree distribution. The Preferential Attachment Model (Barab´asi–Albert, 1999) and the ACL Preferential Attachment

The γ-graph of a graph For a graph G = (V, E), the γ-graph of G, G(γ) = (V (γ), E(γ)), is the reconfiguration graph whose vertex set is the collection of minimum dominating sets, or γ-sets of G, and

Dynamical algebraic combinatorics and independence sets of graphs Dynamical algebraic combinatorics is a relatively new (and fun!) topic, which looks at cyclic group actions on objects from algebraic combinatorics, inspired by some questions coming from dynamical systems. I will give