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A hypergraph Tur\'{a}n problem with no stability
- Publication Year :
- 2019
-
Abstract
- A fundamental barrier in extremal hypergraph theory is the presence of many near-extremal constructions with very different structures. Indeed, the classical constructions due to Kostochka imply that the notorious extremal problem for the tetrahedron exhibits this phenomenon assuming Tur\'an's conjecture. Our main result is to construct a finite family of triple systems $\mathcal{M}$, determine its Tur\'{a}n number, and prove that there are two near-extremal $\mathcal{M}$-free constructions that are far from each other in edit-distance. This is the first extremal result for a hypergraph family that fails to have a corresponding stability theorem.<br />Comment: revised according to referees' suggestions
- Subjects :
- Mathematics - Combinatorics
05D05, 05C35, 05C65
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1911.07969
- Document Type :
- Working Paper