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• W3150072531 abstract "We present a method which provides a unified framework for most stability theorems that have been proved in graph and hypergraph theory. Our main result reduces stability for a large class of hypergraph problems to the simpler question of checking that a hypergraph H with large minimum degree that omits the forbidden structures is vertex-extendable. This means that if v is a vertex of H and H−v is a subgraph of the extremal configuration(s), then H is also a subgraph of the extremal configuration(s). In many cases vertex-extendability is quite easy to verify. We illustrate our approach by giving new short proofs of hypergraph stability results of Pikhurko, Hefetz-Keevash, Brandt-Irwin-Jiang, Bene Watts-Norin-Yepremyan and others. Since our method always yields minimum degree stability, which is the strongest form of stability, in some of these cases our stability results are stronger than what was known earlier. Along the way, we clarify the different notions of stability that have been previously studied." @default.
• W3150072531 created "2021-04-13" @default.
• W3150072531 creator A5042704391 @default.
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• W3150072531 date "2023-01-01" @default.
• W3150072531 modified "2023-10-14" @default.
• W3150072531 title "A unified approach to hypergraph stability" @default.
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• W3150072531 doi "https://doi.org/10.1016/j.jctb.2022.08.008" @default.
• W3150072531 hasPublicationYear "2023" @default.
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