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Triple systems with no three triples spanning at most five points.
- Source :
-
Bulletin of the London Mathematical Society . Apr2019, Vol. 51 Issue 2, p230-236. 7p. - Publication Year :
- 2019
-
Abstract
- We show that the maximum number of triples on n points, if no three triples span at most five points, is (1±o(1))n2/5. More generally, let f(r)(n;k,s) be the maximum number of edges in an r‐uniform hypergraph on n vertices not containing a subgraph with k vertices and s edges. In 1973, Brown, Erdős and Sós conjectured that the limit limn→∞n−2f(3)(n;k,k−2) exists for all k. They proved this for k=4, where the limit is 1/6 and the extremal examples are Steiner triple systems. We prove the conjecture for k=5 and show that the limit is 1/5. The upper bound is established via a simple optimisation problem. For the lower bound, we use approximate H‐decompositions of Kn for a suitably defined graph H. [ABSTRACT FROM AUTHOR]
- Subjects :
- *STEINER systems
*LOGICAL prediction
Subjects
Details
- Language :
- English
- ISSN :
- 00246093
- Volume :
- 51
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Bulletin of the London Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 135666671
- Full Text :
- https://doi.org/10.1112/blms.12224