Let f(r,p,t) (p > t ≥ 1, r ≥ 2) be the maximum of the cardinality of a minimum transversal over all r-uniform hypergraphs H possessing the property that every subhypergraph of with p edges has a transversal of size t. The values of f (r,p,2) for p=3, 4, 5, 6 were found in  and hounds on f (r, 7, 2) are given in . Here we prove that f (r,p,2) ≤ 1.3 r/p0.5-o(p0.5) for large p and huge r.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Computational Mathematics