The largest transversal numbers of uniform hypergraphs
If \(H\) is an \(r\)-uniform hypergraph of order \(p\) without \((r+ 1)\)-cliques, then the transversal number of \(H\) has an upper bound in terms of \(c= p- 2r\). As corollaries of this result, lower bounds for the largest order of \(r\)-uniform hypergraphs with specified transversal number and for the stability number of triangle-free graphs are given.
scientific article; zbMATH DE number 858063