V. Rodl

activity

20212026

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13 papers · 1 filter

math.CO2026

Canonical Ramsey theorem for graphs with clean intersections

Matías Azócar Carvajal, Ayush Basu, Christian Reiher +3

Extending earlier results of Nešetřil and Rödl [Selective graphs and hypergraphs, Ann. Discrete Math. 3 (1978), 181--189], we show that for every ordered graph $F$ there exist an o…

math.CO2026

On Ramsey number of Steiner systems

Ayush Basu, Daniel Dobak, Vojtěch Rödl +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

Unavoidable subgraphs in Ramsey graphs

Christian Reiher, Vojtěch Rödl, Mathias Schacht

We study subgraphs that appear in large Ramsey graphs for a given graph $F$ . The recent girth Ramsey theorem of the first two authors asserts that there are Ramsey graphs such that…

math.CO2025

Relative Turán densities of ordered graphs

Christian Reiher, Vojtěch Rödl, Marcelo Sales +1

We introduce a modification of the Turán density of ordered graphs and investigate this graph parameter.

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…