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Cancellative hypergraphs and Steiner triple systems.
- Source :
-
Journal of Combinatorial Theory - Series B . Jul2024, Vol. 167, p303-337. 35p. - Publication Year :
- 2024
-
Abstract
- A triple system is cancellative if it does not contain three distinct sets A , B , C such that the symmetric difference of A and B is contained in C. We show that every cancellative triple system H that satisfies a particular inequality between the sizes of H and its shadow must be structurally close to the balanced blowup of some Steiner triple system. Our result contains a stability theorem for cancellative triple systems due to Keevash and Mubayi as a special case. It also implies that the boundary of the feasible region of cancellative triple systems has infinitely many local maxima, thus giving the first example showing this phenomenon. [ABSTRACT FROM AUTHOR]
- Subjects :
- *STEINER systems
*HYPERGRAPHS
Subjects
Details
- Language :
- English
- ISSN :
- 00958956
- Volume :
- 167
- Database :
- Academic Search Index
- Journal :
- Journal of Combinatorial Theory - Series B
- Publication Type :
- Academic Journal
- Accession number :
- 176991277
- Full Text :
- https://doi.org/10.1016/j.jctb.2024.03.006