On the Ramsey Number of Sparse 3-Graphs

Abstract

We consider a hypergraph generalization of a conjecture of Burr and Erdős concerning the Ramsey number of graphs with bounded degree. It was shown by Chvatal, Rodl, Trotter, and Szemeredi [The Ramsey number of a graph with bounded maximum degree, J. Combin. Theory Ser. B 34 (1983), no. 3, 239–243] that the Ramsey number R(G) of a graph G of bounded maximum degree is linear in |V(G)|. We derive the analogous result for 3-uniform hypergraphs.