@article{Conlon2009RamseyNO,
title={Ramsey numbers of sparse hypergraphs},
author={David Conlon and Jacob Fox and Benny Sudakov},
journal={Random Struct. Algorithms},
year={2009},
volume={35},
pages={1-14}
}

We give a short proof that any k-uniform hypergraph H on n vertices with bounded degree ∆ has Ramsey number at most c(∆, k)n, for an appropriate constant c(∆, k). This result was recently proved by several authors, but those proofs are all based on applications of the hypergraph regularity method. Here we give a much simpler, self-contained proof which uses new techniques developed recently by the authors together with an argument of Kostochka and Rödl. Moreover, our method demonstrates that… CONTINUE READING