Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.18832 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- A typical Dirac-type problem in extremal graph theory is to determine the minimum degree threshold for a graph $G$ to have a spanning subgraph $H$, e.g. the Dirac theorem. A natural following up problem would be to seek an $H$-factor, which a spanning set of vertex-disjoint copies of $H$. In this short note, we present a method of obtaining an upper bound on the minimum degree threshold for an $H$-factor from one for finding a spanning copy of $H$. As an application, we proved that, for all $\varepsilon>0$ and $\ell$ sufficiently large, any oriented graph $G$ on $\ell m$ vertices with minimum semi-degree $δ^0(G) \ge (3/8+ \varepsilon) k \ell$ contains a $C_\ell$-factor, where $C_\ell$ is an arbitrary orientation of a cycle on $\ell$ vertices. This improves a result of Wang, Yan and Zhang.