Allan’s research interests lie in extremal and probabilistic graph theory. A typical problem in this field is to determine the necessary condition for the existence of a fixed spanning subgraph (e.g. Hamilton cycle) in a graph, edge-coloured graph, orientated graph or hypergraph.
The current focus of his research is on graph decompositions. For example (jointly with B. Csaba, D. Kuhn, D. Osthus and A. Treglown), he recently proved the 1-factorisation conjecture and Hamilton decomposition conjecture for large graphs.