Sufficient conditions for perfect mixed tilings

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 perfec...

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Hauptverfasser: Hurley, Eoin (VerfasserIn) , Joos, Felix (VerfasserIn) , Lang, Richard (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: January 2025
In: Journal of combinatorial theory
Year: 2025, Jahrgang: 170, Pages: 128-188
DOI:10.1016/j.jctb.2024.08.007
Online-Zugang:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.jctb.2024.08.007
Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S009589562400073X
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Verfasserangaben:Eoin Hurley, Felix Joos, Richard Lang

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520 |a 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. 
650 4 |a Minimum degree conditions 
650 4 |a Perfect tiling 
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