Richard's research interests lie in the field of Extremal Graph Theory. A significant area of research in this field is to determine the existence of a fixed large or spanning subgraph within a graph, directed graph or hypergraph.
For example, Richard's recent work includes the use of a randomised embedding algorithm to prove Sumner's Universal Tournament Conjecture for large tournaments. This states (loosely) that any sufficiently large tournament contains any tree on roughly half the number of vertices.
More recently his focus has been on finding perfect matchings and packing's in hypergraphs.
Dr Richard Mycroft profile