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Published August 20, 2019 | Submitted
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Hedgehogs are not colour blind


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.

Additional Information

Conlon research supported by a Royal Society University Research Fellowship. Fox research supported by a Packard Fellowship, by NSF Career Award DMS-1352121 and by an Alfred P. Sloan Fellowship. Rödl research partially supported by NSF grants DMS-1102086 and DMS-1301698.

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August 20, 2023
August 20, 2023