16 papers
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 there exist an o…
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…
Unavoidable subgraphs in Ramsey graphs
Christian Reiher, Vojtěch Rödl, Mathias Schacht
We study subgraphs that appear in large Ramsey graphs for a given graph . The recent girth Ramsey theorem of the first two authors asserts that there are Ramsey graphs such that…
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.
A lower bound on the Ramsey number
Pavel Pudlák, Vojtěch Rödl, William J. Wesley
We will prove that , where is the tower function defined by and . We also give pro…
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…
Ramsey-type problems for generalised Sidon sets
Christian Reiher, Vojtěch Rödl, Mathias Schacht
We establish the existence of generalised Sidon sets enjoying additional Ramsey-type properties, which are motivated by questions of Erdős and Newman and of Alon and Erdős.
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…
The girth Ramsey theorem
Christian Reiher, Vojtěch Rödl
Given a hypergraph and a number of colours , there exists a hypergraph of the same girth satisfying . Moreover, for every linear hypergraph t…
On the Ramsey number of daisies I
Pavel Pudlák, Vojtěch Rödl, Marcelo Sales
Daisies are a special type of hypergraphs introduced by Bollobás, Leader and Malvenuto. An -daisy determined by a pair of disjoint sets and is the -uniform hype…
Turán density of cliques of order five in -uniform hypergraphs with quasirandom links
Sören Berger, Simón Piga, Christian Reiher +2
We show that -uniform hypergraphs with the property that all vertices have a quasirandom link graph with density bigger than contain a clique on five vertices. This result…
Colourful matchings
Andrii Arman, Vojtěch Rödl, Marcelo Tadeu Sales
Suppose a committee consisting of three members has to match candidates to different positions. Each member of the committee proposes a matching, however the proposed match…
Ramsey Partial Orders from Acyclic Graphs
Jaroslav Nešetřil, Vojtěch Rödl
We prove that finite partial orders with a linear extension form a Ramsey class. Our proof is based on the fact that class of acyclic graphs has the Ramsey property and uses the pa…