One of the main questions that arise when studying random and quasi-random structures is which properties P are such that any object that satisfies P "behaves" like a tr...
Let H be a graph, and let CH(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating CH(G). Previous res...
We consider the problem of finding a sparse set of edges containing the minimum spanning tree (MST) of a random subgraph of G with high probability. The two random models that we ...
We consider the problem of generating a random q-colouring of a graph G = (V, E). We consider the simple Glauber Dynamics chain. We show that if for all v V the average degree of...
For any graph G, the k-improper chromatic number k (G) is the smallest number of colours used in a colouring of G such that each colour class induces a subgraph of maximum degree ...