Some remarks on vertex Folkman numbers for hypergraphs

Let F ( r , G ) be the least order of H such that the clique numbers of H and G are equal and any r -coloring of the vertices of H yields a monochromatic and induced copy of G . The problem of bounding of F ( r , G ) was studied by several authors and it is well understood. In this note, we extend those results to uniform hypergraphs.