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Problem 207
For any , if is sufficiently large and then there exists a 3-uniform hypergraph on vertices such that every pair of vertices is contained in exactly one edge (i.e. the graph is a Steiner triple system) and for any any collection of edges contains at least vertices.
Source: erdosproblems.com/207
- Combinatorics
- Hypergraphs
Status
Solved, ProvedAn accepted solution exists. The statement is true.
The site labels the problem proved, crediting Kwan, Sah, Sawhney and Simkin [KSSS22b]. The accepted claim is Steiner triple systems of arbitrarily high girth.