Year: 2026
Type: article
Abstract: ABSTRACT 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.
Source: Journal of Graph Theory
DOI: 10.1002/jgt.70147
Author: Allan Lo
Institution: University of Birmingham
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,150
OpenAlex ID: W4416258562
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