The largest transversal numbers of uniform hypergraphs Original Research Article

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 the parameter c = p − 2r. As corollaries of the main theorem, 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 as well.