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