Rafael Filipe

collaborators

4 papers

math.CO2026

Off-Diagonal Induced Ramsey Numbers

Bruno Andrades, Marcelo Campos, Rafael Filipe +1

Given graphs $F$ and $H$ , the induced Ramsey number $r_{ind} (F, H)$ is the smallest integer $n$ for which there exists a graph $G$ on $n$ vertices such that every red-blue…

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

A note on the maximum ratio between chromatic number and clique number

Igor Araujo, Rafael Filipe, Rafael Miyazaki

Let $f (n)$ be the maximum, over all graphs $G$ on $n$ vertices, of the ratio $\frac{χ ( G )}{ω ( G )}$ , where $χ (G)$ denotes the chromatic number of $G$ and $ω (G)$ the clique number of $…

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…