We exhibit a family of 3-uniform hypergraphs with the property that their 2-colour Ramsey numbers grow polynomially in the number of vertices, while their 4-colour Ramsey numbers grow exponentially. This is the first example of a class of hypergraphs whose Ramsey numbers show a strong dependence on the number of colours.
@article{arxiv.1511.00563,
title = {Hedgehogs are not colour blind},
author = {David Conlon and Jacob Fox and Vojtěch Rödl},
journal= {arXiv preprint arXiv:1511.00563},
year = {2015}
}