V. Rodl

activity

20162026

collaborators

Showing 2024Show all

6 papers · 1 filter

math.CO2024

A lower bound on the Ramsey number $R_{k} (k + 1, k + 1)$

Pavel Pudlák, Vojtěch Rödl, William J. Wesley

We will prove that $R_{k} (k + 1, k + 1) \geq 4 t w_{⌊ k /4 ⌋ - 3} (2)$ , where $tw$ is the tower function defined by $tw_{1} (x) = x$ and $tw_{i + 1} (x) = 2^{tw_{i} (x)}$ . We also give pro…

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

Ramsey-type problems for generalised Sidon sets

Christian Reiher, Vojtěch Rödl, Mathias Schacht

We establish the existence of generalised Sidon sets enjoying additional Ramsey-type properties, which are motivated by questions of Erdős and Newman and of Alon and Erdős.

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\…

A lower bound on the Ramsey number Rk​(k+1,k+1)

Coloring triangles in graphs

Ramsey-type problems for generalised Sidon sets

The k-representation number of the random graph

Nowhere dense Ramsey sets

Note on set representation of bounded degree hypergaphs

A lower bound on the Ramsey number $R_{k} (k + 1, k + 1)$

The $k$ -representation number of the random graph