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arXiv · 2201.03944

Sufficient conditions for perfect mixed tilings

Eoin Hurley·Felix Joos·Richard Lang
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Abstract

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 K\"uhn 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 Koml\'os in a strong sense.

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Eoin Hurley, Felix Joos, Richard Lang. 2022-01-11. Sufficient conditions for perfect mixed tilings. https://arxiv.org/abs/2201.03944

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