Marcelo Sales

activity

20242026

collaborators

6 papers

math.CO2026

On Ramsey number of Steiner systems

Ayush Basu, Daniel Dobak, VojtÄch RÃ¶dl +1

A $k$ -uniform hypergraph $H$ is called a partial $(k, ℓ)$ -system if every set of $ℓ$ vertices of $V (H)$ is contained in at most one edge of $H$ . We prove the existence of a pa…

math.CO2025

Nowhere dense Ramsey sets

VojtÄch RÃ¶dl, Marcelo Sales

A set of points $S$ in Euclidean space $R^{d}$ is called \textit{Ramsey} if any finite partition of $R^{\infty}$ yields a monochromatic copy of $S$ . While character…

math.CO2025

Relative TurÃ¡n densities of ordered graphs

Christian Reiher, VojtÄch RÃ¶dl, Marcelo Sales +1

We introduce a modification of the TurÃ¡n density of ordered graphs and investigate this graph parameter.

math.CO2024

Note on set representation of bounded degree hypergaphs

Ayush Basu, Griffin Johnston, VojtÄch RÃ¶dl +1

In their classical paper, ErdÅs, Goodman and PÃ³sa studied the representation of a graph with vertex set $[n]$ by a family of subsets $S_{1}, \dots, S_{n}$ with the property that $\{i,…

math.CO2024

Coloring triangles in graphs

Ayush Basu, VojtÄch RÃ¶dl, Marcelo Sales

We study quantitative aspects of the following fact: For every graph $F$ , there exists a graph $G$ with the property that any $2$ -coloring of the triangles of $G$ yields an induced…

math.CO2024

Colouring versus density in integers and Hales-Jewett cubes

Christian Reiher, VojtÄch RÃ¶dl, Marcelo Sales

We construct for every integer $k \geq 3$ and every real $I^¼ \in (0, \frac{k - 1}{k})$ a set of integers $X = X (k, I^¼)$ which, when coloured with finitely many colours, contains a monochr…