Marcelo Campos

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20242026

most citedUpper bounds for multicolour Ramsey numbers

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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

A new lower bound for two-color van der Waerden numbers

Marcelo Campos, Jacob Fox, Carl Schildkraut

The van der Waerden number $w (k)$ is the smallest positive integer $N$ such that every two-coloring of ${1, 2, \dots, N}$ contains a monochromatic $k$ -term arithmetic progression.…

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

A new lower bound for two-color van der Waerden numbers

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