Journal of Combinatorics
Volume 8 (2017)
Guest Editor: Steve Butler (Iowa State University)
Hedgehogs are not colour blind
Pages: 475 – 485
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.
Ramsey numbers, hypergraphs
D. Conlon is supported by a Royal Society University Research Fellowship and by ERC Starting Grant 676632.
J. Fox is supported by a Packard Fellowship, by NSF Career Award DMS-1352121 and by an Alfred P. Sloan Fellowship.
V. Rödl is supported by NSF Grant DMS-1301698.
Paper received on 31 October 2015.