Sufficient conditions for perfect mixed tilings

• Verfasst von: Hurley, Eoin [VerfasserIn]
• Verfasst von: Joos, Felix [VerfasserIn]
• Verfasst von: Lang, Richard [VerfasserIn]
• Titel: Sufficient conditions for perfect mixed tilings
• Verf.angabe: Eoin Hurley, Felix Joos, Richard Lang
• E-Jahr: 2025
• Jahr: January 2025
• Umfang: 61 S.
• Fussnoten: Online veröffentlicht: 24. September 2024 ; Gesehen am 26.02.2025
• Titel Quelle: Enthalten in: Journal of combinatorial theory
• Ort Quelle: Orlando, Fla. : Academic Press, 1971
• Jahr Quelle: 2025
• Band/Heft Quelle: 170(2025), Seite 128-188
• DOI: doi:10.1016/j.jctb.2024.08.007
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Minimum degree conditions
• Sach-SW: Perfect tiling
• K10plus-PPN: 1918606447

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 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.