A Stability Result for Almost Perfect Matchings
ABSTRACT Let be three integers and be a sufficiently small positive number such that , , and . A ‐graph is called non‐trivial if it has no isolated vertex. In this paper, we determine the maximum number of edges in a non‐trivial ‐graph with vertices and matching number at most . This result confirms a conjecture proposed by Frankl (On non‐trivial families without a perfect matching, European J. Combin ., 84 (2020), 103044) for the case when is sufficiently large.
Authors
- Hongliang Lu (ORCID: https://orcid.org/0000-0003-4447-2416)
- Mingyang Guo
Institutions
- Zhengzhou University (CN)
- Xi'an Jiaotong University (CN)
Publication Details
- Journal
- Journal of Graph Theory
- Published
- 2026-02-18
- DOI
- https://doi.org/10.1002/jgt.70007
- Primary Topic
- Limits and Structures in Graph Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Natural Science Foundation of China