Improved bounds for zeros of the chromatic polynomial on bounded degree graphs About 20 years ago Sokal proved that there exists a constant C so that for any graph G, all of the complex zeros of its chromatic polynomial are

2017 saw the centennial of William Tutte, one of the greatest mathematicians of modern times.  One of the testimonies to Tutte’s genius is that nearly everything he did proved to be a catalyst, triggering an explosion of further investigations and

I will discuss a few examples where considering loops leads to interesting insights, often allowing unifying existing results. These examples will include cops and robbers games, graph homomorphisms, variants of interval and chordal graphs, and versions of domination. Join Zoom

There are many results about triangles in graphs, but the property that every edge in a graph is in at least one triangle seems not to have been studied before. The 4-regular case was quickly solved collaboratively following an internet

I will begin by giving a general overview of what it means to find monarchs for excluded minor classes of graphs and matroids. In a paper that appeared in 2018, I used the Strong Splitter Theorem to give a short

Spanning Trees and Graphs Embedded in Surfaces To what extent is a graph determined by the trees contained in it? That is, if we know the edge sets of each of the spanning trees (i.e., maximal acyclic subgraphs) in a

Robustness of Complex Networks Network Science aims to understand the graph structure of networks and the dynamic processes that take place on networks. Examples of processes on networks are transport of items (IP packets with digitalized  information, cars, containers) and diffusion (epidemics, electric current,

Mutually Orthogonal Cycle Systems A $k$-cycle system of order $n$ is a set of $k$-cycles whose edges partition the edge set of $K_n$.  We say that two cycle systems $\mathcal{C}$ and $\mathcal{C}'$ are {\em orthogonal} if every cycle in $\mathcal{C}$

The Orthogonal Colouring Game The Orthogonal Colouring Game is a combinatorial game in which two players alternately colour vertices of a pair of isomorphic graphs while respecting the properness and the orthogonality of the colouring. Each player aims to maximize

Reconfiguration for Dominating Sets Given a problem and a set of feasible solutions to that problem, the associated  reconfiguration problem involves determining whether one feasible solution to the original problem can be transformed to a different feasible solution through a