Transversals in uniform hypergraphs with property \((p,2)\)
Consider the class of all those \(r\)-uniform hypergraphs where every subhypergraph with \(p\) edges has a transversal of size \(t\). Let \(f(r,p,t)\) be the maximum of the cardinality of a minimum transversal over all hypergraphs in this class. The values of \(f(r,p,2)\) were known for \(p=3,4,5,6\) and a bound was known for \(p=7\). Here the author proves that \(f(r,p,2) \leq 1.3 \cdot r/(p^{0.5}-o(p^{0.5}))\) for large \(p\) and huge \(r\).
scientific article; zbMATH DE number 1822337