Sufficient conditions for perfect mixed tilings
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910661536120832 |
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| author | Hurley, Eoin Joos, Felix Lang, Richard |
| author_facet | Hurley, Eoin Joos, Felix Lang, Richard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_03944 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Sufficient conditions for perfect mixed tilings Hurley, Eoin Joos, Felix Lang, Richard Combinatorics Discrete Mathematics 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. |
| title | Sufficient conditions for perfect mixed tilings |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2201.03944 |