Tower Gaps in Multicolour Ramsey Numbers

Open Access
Authors
Publication date 21-09-2023
Journal Forum of Mathematics, Sigma
Article number e84
Volume | Issue number 11
Number of pages 15
Organisations
  • Faculty of Science (FNWI) - Korteweg-de Vries Institute for Mathematics (KdVI)
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.

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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