English

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 HH 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 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 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

R2 v1 2026-06-24T08:46:25.097Z