Marcelo Sales

activity

20232026

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Showing 2024Show all

4 papers · 1 filter

math.CO2024

Coloring triangles in graphs

Ayush Basu, Vojtěch Rödl, 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

The $k$ -representation number of the random graph

Ayush Basu, Vojtěch Rödl, Marcelo Sales

The $k$ -representation number of a graph $G$ is the minimum cardinality of the system of vertex subsets with the property that every edge of $G$ is covered at least $k$ times while…

math.CO2024

Nowhere dense Ramsey sets

Vojtěch Rödl, 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.CO2024

Note on set representation of bounded degree hypergaphs

Ayush Basu, Griffin Johnston, Vojtěch Rödl +1

In their classical paper, Erdős, Goodman and Pósa 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,j\…

Coloring triangles in graphs

The k-representation number of the random graph

Nowhere dense Ramsey sets

Note on set representation of bounded degree hypergaphs

The $k$ -representation number of the random graph