Robert Morris

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20122026

most citedUpper bounds for multicolour Ramsey numbers

2 citations · 2 across the 5 of their papers we have counts for

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math.CO2026

On the multicolour Ramsey numbers $R (3, 3, k)$

Bruno Andrades, Marcelo Campos, Robert Morris

In this paper we determine the Ramsey number $R (3, 3, k)$ up to a constant factor, showing that $R (3, 3, k) = Θ (\frac{k ^{3}}{( lo g k ) ^{2}}) .$ The proof of the lower bound com…

math.CO2026

On the Erdős-Rogers function

Robert Morris, Julian Sahasrabudhe, Jacques Verstraëte

We show that the Erdős-Rogers function $f_{s, s + 1} (n)$ satisfies $f_{s, s + 1} (n) = Θ (n lo g n)$ for every $s \geq 2$ . More precisely, we construct a $K_{s + 1}$ -free graph on…

math.CO2026

Some recent results in Ramsey theory

Robert Morris

The purpose of this survey is to provide a gentle introduction to several recent breakthroughs in graph Ramsey theory. In particular, we will outline the proofs (due to various gro…

On the multicolour Ramsey numbers R(3,3,k)

On the Erdős-Rogers function

Some recent results in Ramsey theory

On the multicolour Ramsey numbers $R (3, 3, k)$