Some remarks on vertex Folkman numbers for hypergraphs

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