# Perfect one-factorisations

**Project level:** PhD

The perfect one-factorisation conjecture (attributed to Kotzig 1964) is that there exists a perfect one-factorisation of every complete graph of even order. To date this has only been shown to be true for two families of complete graphs: those with order one more than a prime or twice a prime. A similar situation exists for perfect one-factorisations of complete bipartite graphs. This project aims to discover new perfect one-factorisations of complete and complete bipartite graphs and will suit students interested in graph theory or design theory (Latin squares).