On Ramsey numbers of uniform hypergraphs with given maximum degree

For every ϵ>0 and every positive integers Δ and r, there exists C=C(ϵ,Δ,r) such that the Ramsey number, R(H,H) of any r-uniform hypergraph H with maximum degree at most Δ is at most C|V(H)|1+ϵ.