Ayush Basu

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math.CO2026

Regularity method for hypergraphs with $4$ -cycle-free links

Ayush Basu, Christian Reiher, Vojtěch Rödl +1

We extend the hypergraph regularity method to sparse $3$ -uniform hypergraphs whose vertex links are $C_{4}$ -free. In other words, we consider hypergraphs $H = (V, E)$ that are $K_{1,2,2…

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.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 number of cliques in hypergraphs with forbidden subgraphs

Ayush Basu, Vojtech Rodl, Yi Zhao

We study the maximum number of $r$ -vertex cliques in $(r - 1)$ -uniform hypergraphs not containing complete $r$ -partite hypergraphs $K_{r}^{(r - 1)} (a_{1}, \dots, a_{r})$ . By using the hyperg…

Regularity method for hypergraphs with 4-cycle-free links

Canonical Ramsey theorem for graphs with clean intersections

On Ramsey number of Steiner systems

Coloring triangles in graphs

The number of cliques in hypergraphs with forbidden subgraphs

Regularity method for hypergraphs with $4$ -cycle-free links