6 papers · 1 filter
Regularity method for hypergraphs with -cycle-free links
Ayush Basu, Christian Reiher, Vojtěch Rödl +1
We extend the hypergraph regularity method to sparse -uniform hypergraphs whose vertex links are -free. In other words, we consider hypergraphs that are $K_{1,2,2…
Canonical Ramsey theorem for graphs with clean intersections
MatÃas Azócar Carvajal, Ayush Basu, Christian Reiher +3
Extending earlier results of NeÅ¡etÅil and Rödl [Selective graphs and hypergraphs, Ann. Discrete Math. 3 (1978), 181--189], we show that for every ordered graph there exist a…
On Ramsey number of Steiner systems
Ayush Basu, Daniel Dobak, VojtÄch Rödl +1
A -uniform hypergraph is called a partial -system if every set of vertices of is contained in at most one edge of . We prove the existence of a pa…
The number of cliques in hypergraphs with forbidden subgraphs
Ayush Basu, Vojtech Rodl, Yi Zhao
We study the maximum number of -vertex cliques in -uniform hypergraphs not containing complete -partite hypergraphs . By using the hyperg…
Note on set representation of bounded degree hypergaphs
Ayush Basu, Griffin Johnston, VojtÄch Rödl +1
In their classical paper, ErdÅs, Goodman and Pósa studied the representation of a graph with vertex set by a family of subsets with the property that $\{i,…
Coloring triangles in graphs
Ayush Basu, VojtÄch Rödl, Marcelo Sales
We study quantitative aspects of the following fact: For every graph , there exists a graph with the property that any -coloring of the triangles of yields an induced…