Year: 2026
Type: article
Abstract: 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.
Source: Journal of Graph Theory
DOI: 10.1002/jgt.70007
Authors: Mingyang Guo, Hongliang Lu
Institutions: Zhengzhou University, Xi'an Jiaotong University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Award: G6216466512
OpenAlex ID: W7130327166