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

In this talk, I will show regions that contain no complex zeros the edge-cover polynomials of hypergraphs. The edge cover polynomial of a graph $G$ is the generating function of edges that covers $V(G)$. It is known that the zeros

About a year ago Jason Brown spoke in our seminar (of the university of Amsterdam) about the two-terminal reliability polynomial and left us with some questions about the closure of the complex zeros of all such polynomials (the zero-locus). In

We study the algebraic connectivity for several classes of random semi-regular graphs. For large random semi-regular bipartite graphs, we explicitly compute both their algebraic connectivity and as well as the full spectrum distribution. For an integer d in , we

Extremal questions for vertex colorings of graphs For graphs $G$ and $H$, an $H$-coloring of $G$ is a map from the vertices of $G$ to the vertices of $H$ so that an edge in $G$ is mapped to an edge