Ramsey-type numbers involving graphs and hypergraphs with large girth

For a set of integers S, define to be the k-uniform hypergraph with vertex set S and hyperedges corresponding the set of all arithmetic progression of length k in S. Similarly, for a graph H, define to be the -uniform hypergaph on the vertex ser E(H) with hyperedges corresponding to the edge sets of all copies of Kk in H. Also, we say that a k-uniform hypergraph has girth at least g if any h edges (1≤h