Discrete Mathematics· 2026Q1
Stability results for Berge-matching in hypergraphs
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- Q1SCImago
- 2026year
Short summary
Hypergraphs with nearly the maximum number of edges for Berge-M_k, but without Berge-M_k, are structurally close to specific graphs.
AI-generated from the title and abstract; the full text is not read.
Key points
- Hypergraphs lacking Berge-M_k but having near-extremal edge counts are structurally constrained.
- The result implies that such hypergraphs are 'close' to specific graph structures.
- This work provides a stability version of the Erdős-Gallai theorem for hypergraphs.
AI-generated from the title and abstract; the full text is not read.
Abstract
Given a graph F , a hypergraph is called a Berge- F if it can be obtained by expanding each edge of F into a hyperedge containing it. Let M k denote the matching of size k . Kang, Ni, and Shan [12] determined the Turán number of Berge- M k . Our main result shows that if an r -uniform hypergraph H on n vertices has nearly as many edges as the extremal in their theorem without containing Berge- M k , then H must be structurally close to certain well-specified graphs. Meanwhile, our result also implies several stability results, such as the stability version of the well-known Erdős-Gallai theorem (Erdős and Gallai, 1959 [5] ).
The authors' abstract, as published at the source. Discrete Mathematics, 2026 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics