Tower Gaps in Multicolour Ramsey Numbers
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| Publication date | 21-09-2023 |
| Journal | Forum of Mathematics, Sigma |
| Article number | e84 |
| Volume | Issue number | 11 |
| Number of pages | 15 |
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| Abstract |
Resolving a problem of Conlon, Fox and Rödl, we construct a family of hypergraphs with arbitrarily large tower height separation between their 2-colour and q-colour Ramsey numbers. The main lemma underlying this construction is a new variant of the Erdős–Hajnal stepping-up lemma for a generalized Ramsey number rk(t;q,p), which we define as the smallest integer n such that every q-colouring of the k-sets on n vertices contains a set of t vertices spanning fewer than p colours. Our results provide the first tower-type lower bounds on these numbers.
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| Document type | Article |
| Note | Publisher Copyright: © The Author(s), 2023. Published by Cambridge University Press. |
| Language | English |
| Published at | https://doi.org/10.1017/fms.2023.89 |
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Tower Gaps in Multicolour Ramsey Numbers
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