Sufficient conditions for perfect mixed tilings
Combinatorics
2024-10-24 v3 Discrete Mathematics
Abstract
We develop a method to study sufficient conditions for perfect mixed tilings. Our framework allows the embedding of bounded degree graphs with components of sublinear order. As a corollary, we recover and extend the work of K\"uhn and Osthus regarding sufficient minimum degree conditions for perfect -tilings (for an arbitrary fixed graph ) by replacing the -tiling with the aforementioned graphs . Moreover, we obtain analogous results for degree sequences and in the setting of uniformly dense graphs. Finally, we asymptotically resolve a conjecture of Koml\'os in a strong sense.
Keywords
Cite
@article{arxiv.2201.03944,
title = {Sufficient conditions for perfect mixed tilings},
author = {Eoin Hurley and Felix Joos and Richard Lang},
journal= {arXiv preprint arXiv:2201.03944},
year = {2024}
}
Comments
40 pages + 3 pages appendix