Marcelo Campos

activity

20242026

collaborators

4 papers

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.…

math.CO2026

Upper bounds for multicolour Ramsey numbers

Paul Balister, BÃ©la BollobÃ¡s, Marcelo Campos +5

The $r$ -colour Ramsey number $R_{r} (k)$ is the minimum $n \in N$ such that every $r$ -colouring of the edges of the complete graph $K_{n}$ on $n$ vertices contains a monochroma…

math.CO2025

An exponential upper bound for induced Ramsey numbers

Lucas AragÃ£o, Marcelo Campos, Gabriel Dahia +2

The induced Ramsey number $R_{ind} (H; r)$ of a graph $H$ is the minimum number $N$ such that there exists a graph with $N$ vertices for which all $r$ -colourings of its edg…

math.CO2024

On the independence number of sparser random Cayley graphs

Marcelo Campos, Gabriel Dahia, JoÃ£o Pedro Marciano

The Cayley sum graph $I^_{A}$ of a set $A \subseteq Z_{n}$ is defined to have vertex set $Z_{n}$ and an edge between two distinct vertices $x, y \in Z_{n}$ if $x…