From Finding a Spanning Subgraph H to an H‐Factor

A typical Dirac‐type problem in extremal graph theory is to determine the minimum degree threshold for a graph to have a spanning subgraph , for example, the Dirac theorem. A natural follow‐up problem is to seek an ‐factor, which is a spanning set of vertex‐disjoint copies of . In this short note, we present a method for obtaining an upper bound on the minimum degree threshold for an ‐factor from one for finding a spanning copy of . As an application, we prove that, for all and sufficiently large , any oriented graph on vertices with minimum semi‐degree contains a ‐factor, where is an arbitrary orientation of a cycle on vertices. This improves a result of Wang, Yan and Zhang.