Sufficient conditions for perfect mixed tilings - Hurley, Eoin; Joos, Felix; Lang, Richard (Journal of combinatorial theory, 2025)
We develop a method to study sufficient conditions for perfect mixed tilings. Our framework allows the embedding of bounded degree graphs H 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 F-tilings (for an arbitrary fixed graph F) by replacing the F-tiling with the aforementioned graphs H. Moreover, we obtain analogous results for degree sequences and in the setting of uniformly dense graphs. Finally, we asymptotically resolve a conjecture of Komlós in a strong sense.
Online veröffentlicht: 24. September 2024
Gesehen am 26.02.2025