Ramsey numbers of sparse hypergraphs

@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

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