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 .