Lucas Aragão

activity

20242026

collaborators

4 papers

math.CO2026

Ramsey properties for tilings in random graphs

Lucas AragÃ£o, Xinbu Cheng, Rafael Filipe +3

Let $m H$ be the graph formed by $m$ vertex-disjoint copies of a graph $H$ . Let $G \to (H)_{r}$ denote that, in any $r$ -colouring of the edges of $G$ , there exists a monochromatic cop…

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

The diameter of randomly twisted hypercubes

Lucas AragÃ£o, MaurÃcio Collares, Gabriel Dahia +1

The $n$ -dimensional random twisted hypercube $G_{n}$ is constructed recursively by taking two instances of $G_{n - 1}$ , with any joint distribution, and adding a rand…

math.CO2024

On the number of monochromatic solutions to multiplicative equations

Lucas AragÃ£o, Jonathan Chapman, Miquel Ortega +1

The following question was asked by Prendiville: given an $r$ -colouring of the interval ${2, \dots, N}$ , what is the minimum number of monochromatic solutions of the equation $x…