7 papers · 1 filter
On Ramsey number of Steiner systems
Ayush Basu, Daniel Dobak, Vojtěch 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…
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.
Coloring triangles in graphs
Ayush Basu, Vojtěch 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…
The -representation number of the random graph
Ayush Basu, Vojtěch Rödl, Marcelo Sales
The -representation number of a graph is the minimum cardinality of the system of vertex subsets with the property that every edge of is covered at least times while…
Nowhere dense Ramsey sets
Vojtěch Rödl, Marcelo Sales
A set of points in Euclidean space is called \textit{Ramsey} if any finite partition of yields a monochromatic copy of . While character…
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 by a family of subsets with the property that $\{i,j\…
Colouring versus density in integers and Hales-Jewett cubes
Christian Reiher, Vojtěch Rödl, Marcelo Sales
We construct for every integer and every real a set of integers which, when coloured with finitely many colours, contains a monochrom…