Linear Ramsey Numbers for Bounded-Degree Hypergrahps

We show that the Ramsey number is linear for every uniform hypergraph with bounded degree. This is a hypergraph extension of the famous theorem for ordinary graphs which Chvátal et al. showed in 1983. While Cooley et al. showed it for the 2-color case recently and independently from the author, our theorem contains the multicolor case and our proof is simple and provides a stronger embedding lemma without depending on heavy theorems by Rödl-Schacht [18] that their proof is based on.