Ayush Basu

activity

20242026

collaborators

5 papers

math.CO2026

Canonical Ramsey theorem for graphs with clean intersections

MatÃas AzÃ³car Carvajal, Ayush Basu, Christian Reiher +3

Extending earlier results of NeÅ¡etÅil and RÃ¶dl [Selective graphs and hypergraphs, Ann. Discrete Math. 3 (1978), 181--189], we show that for every ordered graph $F$ there exist a…

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

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…

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…