Cycle tilings and $H$-factors in directed graphs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917274722500608 |
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| author | Molla, Theodore Treglown, Andrew |
| author_facet | Molla, Theodore Treglown, Andrew |
| contents | We prove several results concerning cycle tilings and $H$-factors in digraphs. We provide a minimum semi-degree condition for forcing a digraph to contain a given spanning collection of vertex-disjoint orientations of cycles. Our result is asymptotically best possible for odd cycles and can be viewed as a digraph analogue of the El-Zahar conjecture. In addition, we asymptotically determine the minimum degree threshold for forcing an $H$-factor in a digraph for a range of digraphs $H$, including the cases when $H$ is a tree or anti-directed cycle. Furthermore, an asymptotically exact Ore-type result for forcing a transitive tournament factor in a digraph is proven. Several related open problems are also highlighted. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13737 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cycle tilings and $H$-factors in directed graphs Molla, Theodore Treglown, Andrew Combinatorics We prove several results concerning cycle tilings and $H$-factors in digraphs. We provide a minimum semi-degree condition for forcing a digraph to contain a given spanning collection of vertex-disjoint orientations of cycles. Our result is asymptotically best possible for odd cycles and can be viewed as a digraph analogue of the El-Zahar conjecture. In addition, we asymptotically determine the minimum degree threshold for forcing an $H$-factor in a digraph for a range of digraphs $H$, including the cases when $H$ is a tree or anti-directed cycle. Furthermore, an asymptotically exact Ore-type result for forcing a transitive tournament factor in a digraph is proven. Several related open problems are also highlighted. |
| title | Cycle tilings and $H$-factors in directed graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.13737 |