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