- Combinatorics, especially Extremal and Probabilistic Graph Theory
The main research area of Deryk Osthus is combinatorics. He has worked on random graphs, randomized algorithms and extremal graph theory.
More recent results include:
In 2016 (jointly with S. Glock, D. Kühn and A. Lo) he gave a combinatorial proof of the existence of designs and in 2017 the same team extended this to prove the existence of F-designs for arbitrary hypergraphs F. With F. Joos, S. Glock and D. Kühn, he used the latter to prove a conjecture of Chung-Diaconis-Graham on Euler tours in hypergraphs;
In 2018 (jointly with S. Glock, F. Joos, J. Kim, D. Kühn) he resolved the Oberwolfach problem on decomposing complete graphs into cycle factors for all large n;
In 2021 (jointly with D. Kang, T. Kelly, D. Kühn and A. Methuku), he proved the Erdos-Faber-Lovasz conjecture on edge-colouring linear hypergraphs.