Speaker: Eoin Hurley (Universität Heidelberg)
We develop a method to study sufficient conditions for perfect mixed tilings. Our framework allows the embedding of bounded degree graphs HH with components of sublinear order. As a corollary, we recover and extend the work of Kühn and Osthus regarding sufficient minimum degree conditions for perfect FF-tilings (for an arbitrary fixed graph FF) by replacing the FF-tiling with the aforementioned graphs HH. Moreover, we obtain analogous results for degree sequences. Finally, we asymptotically resolve a conjecture of Komlós in a strong sense.
The paper was joint work with Felix Joos and Richard Lang, and can be found here https://arxiv.org/abs/2201.03944