Lucas Aragão

activity

20232026

collaborators

4 papers

math.CO2026

Ramsey properties for tilings in random graphs

Lucas Aragão, 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 Aragão, 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

Degree conditions for Ramsey goodness of paths

Lucas Aragão, João Pedro Marciano, Walner Mendonça

A classical result of Chvátal implies that if $n \geq (r - 1) (t - 1) + 1$ , then any colouring of the edges of $K_{n}$ in red and blue contains either a monochromatic red $K_{r}$ or a monoch…

math.CO2023

On the number of monochromatic solutions to multiplicative equations

Lucas Aragão, 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…